..
   Copyright 2021 IRT Saint-Exupéry, https://www.irt-saintexupery.com

   This work is licensed under the Creative Commons Attribution-ShareAlike 4.0
   International License. To view a copy of this license, visit
   http://creativecommons.org/licenses/by-sa/4.0/ or send a letter to Creative
   Commons, PO Box 1866, Mountain View, CA 94042, USA.

.. _gen_opt_algos:

Optimization algorithms
=======================

.. warning::
   Some capabilities may require the :ref:`installation <installation>` of |g| with :ref:`all its features <dependencies>`
   and some others may depend on :ref:`plugins <plugins>`.

.. warning::
   All the features of the wrapped libraries may not be exposed through |g|.


.. note::
   The algorithm settings can be passed to a function of the form

   .. code-block:: python

      function(..., settings_model: Base | None = None, **settings: Any)

   either one by one:

   .. code-block:: python

      function(..., setting_name_1=setting_name_1, setting_name_2=setting_name_2, ...)

   or using the argument name ``"settings"`` and the Pydantic model associated with the algorithm:

   .. code-block:: python

      settings = AlgorithmSettings(setting_name_1=setting_name_1, setting_name_2=setting_name_2, ...)
      function(..., settings_model=settings)





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        <th onclick="sortTable(0)">Algorithm<br/>&#x25B2;&#x25BC;</th>
        <th onclick="sortTable(1)">Library<br/>&#x25B2;&#x25BC;</th>
        <th onclick="sortTable(2)">Name in GEMSEO<br/>&#x25B2;&#x25BC;</th>
        <th onclick="sortTable(3)">Package<br/>&#x25B2;&#x25BC;</th>
        <th onclick="sortTable(4)">Handle equality constraints<br/>&#x25B2;&#x25BC;</th>
        <th onclick="sortTable(5)">Handle inequality constraints<br/>&#x25B2;&#x25BC;</th>
        <th onclick="sortTable(6)">Handle float variables<br/>&#x25B2;&#x25BC;</th>
        <th onclick="sortTable(7)">Handle integer variables<br/>&#x25B2;&#x25BC;</th>
        <th onclick="sortTable(8)">Handle multi-objective<br/>&#x25B2;&#x25BC;</th>
        <th onclick="sortTable(9)">Require gradient<br/>&#x25B2;&#x25BC;</th>
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      <tr>
         <td>Augmented_Lagrangian_order_0</td>
         <td></td>
         <td><a href="#augmented-lagrangian-order-0">Augmented_Lagrangian_order_0</a></td>
         <td><a href="https://gitlab.com/gemseo/dev/gemseo">gemseo</a></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
      </tr>


      <tr>
         <td>Augmented_Lagrangian_order_1</td>
         <td></td>
         <td><a href="#augmented-lagrangian-order-1">Augmented_Lagrangian_order_1</a></td>
         <td><a href="https://gitlab.com/gemseo/dev/gemseo">gemseo</a></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
      </tr>


      <tr>
         <td>Differential evolution</td>
         <td>SciPy Global Optimization</td>
         <td><a href="#differential-evolution">DIFFERENTIAL_EVOLUTION</a></td>
         <td><a href="https://gitlab.com/gemseo/dev/gemseo">gemseo</a></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
      </tr>


      <tr>
         <td>Dual annealing</td>
         <td>SciPy Global Optimization</td>
         <td><a href="#dual-annealing">DUAL_ANNEALING</a></td>
         <td><a href="https://gitlab.com/gemseo/dev/gemseo">gemseo</a></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
      </tr>


      <tr>
         <td>Dual simplex</td>
         <td>SciPy Linear Programming</td>
         <td><a href="#dual-simplex">DUAL_SIMPLEX</a></td>
         <td><a href="https://gitlab.com/gemseo/dev/gemseo">gemseo</a></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
      </tr>


      <tr>
         <td>Interior point method</td>
         <td>SciPy Linear Programming</td>
         <td><a href="#interior-point">INTERIOR_POINT</a></td>
         <td><a href="https://gitlab.com/gemseo/dev/gemseo">gemseo</a></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
      </tr>


      <tr>
         <td>L-BFGS-B</td>
         <td>SciPy Local</td>
         <td><a href="#l-bfgs-b">L-BFGS-B</a></td>
         <td><a href="https://gitlab.com/gemseo/dev/gemseo">gemseo</a></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
      </tr>


      <tr>
         <td>mNBI</td>
         <td>MNBI</td>
         <td><a href="#mnbi">MNBI</a></td>
         <td><a href="https://gitlab.com/gemseo/dev/gemseo">gemseo</a></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
      </tr>


      <tr>
         <td>Multi-start optimization</td>
         <td></td>
         <td><a href="#multistart">MultiStart</a></td>
         <td><a href="https://gitlab.com/gemseo/dev/gemseo">gemseo</a></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
      </tr>


      <tr>
         <td>NELDER-MEAD</td>
         <td>SciPy Local</td>
         <td><a href="#nelder-mead">NELDER-MEAD</a></td>
         <td><a href="https://gitlab.com/gemseo/dev/gemseo">gemseo</a></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
      </tr>


      <tr>
         <td>BFGS</td>
         <td>NLopt</td>
         <td><a href="#nlopt-bfgs">NLOPT_BFGS</a></td>
         <td><a href="https://gitlab.com/gemseo/dev/gemseo">gemseo</a></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
      </tr>


      <tr>
         <td>BOBYQA</td>
         <td>NLopt</td>
         <td><a href="#nlopt-bobyqa">NLOPT_BOBYQA</a></td>
         <td><a href="https://gitlab.com/gemseo/dev/gemseo">gemseo</a></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
      </tr>


      <tr>
         <td>COBYLA</td>
         <td>NLopt</td>
         <td><a href="#nlopt-cobyla">NLOPT_COBYLA</a></td>
         <td><a href="https://gitlab.com/gemseo/dev/gemseo">gemseo</a></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
      </tr>


      <tr>
         <td>MMA</td>
         <td>NLopt</td>
         <td><a href="#nlopt-mma">NLOPT_MMA</a></td>
         <td><a href="https://gitlab.com/gemseo/dev/gemseo">gemseo</a></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
      </tr>


      <tr>
         <td>NEWUOA</td>
         <td>NLopt</td>
         <td><a href="#nlopt-newuoa">NLOPT_NEWUOA</a></td>
         <td><a href="https://gitlab.com/gemseo/dev/gemseo">gemseo</a></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
      </tr>


      <tr>
         <td>SLSQP</td>
         <td>NLopt</td>
         <td><a href="#nlopt-slsqp">NLOPT_SLSQP</a></td>
         <td><a href="https://gitlab.com/gemseo/dev/gemseo">gemseo</a></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
      </tr>


      <tr>
         <td>SHGO</td>
         <td>SciPy Global Optimization</td>
         <td><a href="#shgo">SHGO</a></td>
         <td><a href="https://gitlab.com/gemseo/dev/gemseo">gemseo</a></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
      </tr>


      <tr>
         <td>SLSQP</td>
         <td>SciPy Local</td>
         <td><a href="#slsqp">SLSQP</a></td>
         <td><a href="https://gitlab.com/gemseo/dev/gemseo">gemseo</a></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
      </tr>


      <tr>
         <td>Branch & Cut algorithm</td>
         <td>SciPy Mixed-Integer Linear Programming</td>
         <td><a href="#scipy-milp">Scipy_MILP</a></td>
         <td><a href="https://gitlab.com/gemseo/dev/gemseo">gemseo</a></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
      </tr>


      <tr>
         <td>TNC</td>
         <td>SciPy Local</td>
         <td><a href="#tnc">TNC</a></td>
         <td><a href="https://gitlab.com/gemseo/dev/gemseo">gemseo</a></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:red;font-weight: bold;">&#x2717;</span></td>
         <td><span style="color:green;font-weight: bold;text-align: center;">&#x2713;</span></td>
      </tr>

    </table>
    <br/>



.. _Augmented_Lagrangian_order_0_options:

Augmented_Lagrangian_order_0
----------------------------



Module: :class:`gemseo.algos.opt.augmented_lagrangian.augmented_lagrangian_order_0`


:code:`from gemseo.settings.opt import Augmented_Lagrangian_order_0_Settings`



Augmented Lagrangian algorithm for gradient-less functions.











































































































































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Required settings</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**sub_algorithm_name** : *<class 'str'>*

The name of the optimizer used to solve each sub-problem.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**enable_progress_bar** : *typing.Optional[bool], optional*

Whether to enable the progress bar in the optimization log.

If ``None``, use the global value of ``enable_progress_bar`` (see the
``configure`` function to change it globally).


By default it is set to None.


.. raw:: html

    </li>

    <li>

**eq_tolerance** : *<class 'float'>, optional*

The tolerance on the equality constraints.


By default it is set to 0.01.


.. raw:: html

    </li>

    <li>

**ftol_abs** : *<class 'float'>, optional*

The absolute tolerance on the objective function.


By default it is set to 1e-09.


.. raw:: html

    </li>

    <li>

**ftol_rel** : *<class 'float'>, optional*

The relative tolerance on the objective function.


By default it is set to 1e-09.


.. raw:: html

    </li>

    <li>

**gamma** : *<class 'float'>, optional*

The penalty increase factor.


By default it is set to 1.5.


.. raw:: html

    </li>

    <li>

**ineq_tolerance** : *<class 'float'>, optional*

The tolerance on the inequality constraints.


By default it is set to 0.0001.


.. raw:: html

    </li>

    <li>

**initial_rho** : *<class 'float'>, optional*

The initial penalty value.


By default it is set to 10.0.


.. raw:: html

    </li>

    <li>

**log_problem** : *<class 'bool'>, optional*

Whether to log the definition and result of the problem.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**max_iter** : *<class 'int'>, optional*

The maximum number of iterations.


By default it is set to 1000.


.. raw:: html

    </li>

    <li>

**max_rho** : *<class 'float'>, optional*

The maximum penalty value.


By default it is set to 10000.


.. raw:: html

    </li>

    <li>

**max_time** : *<class 'float'>, optional*

The maximum runtime in seconds, disabled if 0.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**normalize_design_space** : *<class 'bool'>, optional*

Whether to normalize the design space variables between 0 and 1.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**reset_iteration_counters** : *<class 'bool'>, optional*

Whether to reset the iteration counters before each execution.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**round_ints** : *<class 'bool'>, optional*

Whether to round the integer variables.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**scaling_threshold** : *typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional*

The threshold on the reference function value that triggers scaling.

If ``None``, do not scale the functions.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**stop_crit_n_x** : *<class 'int'>, optional*

The minimum number of design vectors to consider in the stopping criteria.


By default it is set to 3.


.. raw:: html

    </li>

    <li>

**store_jacobian** : *<class 'bool'>, optional*

Whether to store the Jacobian matrices in the database.

This argument is ignored when the ``use_database`` option is ``False``.
If a gradient-based algorithm is used,
this option cannot be set along with kkt options.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**sub_algorithm_settings** : *collections.abc.Mapping[str, typing.Any], optional*

The settings of the optimizer used to solve each sub-problem.


By default it is set to {}.


.. raw:: html

    </li>

    <li>

**sub_problem_constraints** : *collections.abc.Iterable[str], optional*

The constraints to keep in the sub-problem.

If ``empty``, all constraints are handled by the Augmented Lagrangian method
which implies that the sub-problem is unconstrained.


By default it is set to ().


.. raw:: html

    </li>

    <li>

**tau** : *<class 'float'>, optional*

The threshold to increase the penalty.


By default it is set to 0.9.


.. raw:: html

    </li>

    <li>

**update_options_callback** : *typing.Optional[typing.Annotated[typing.Callable[[typing.Any], typing.Any], WithJsonSchema(json_schema={}, mode=None)]], optional*

A callable for updating parameters or a function call.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**use_database** : *<class 'bool'>, optional*

Whether to wrap the functions in the database.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_one_line_progress_bar** : *<class 'bool'>, optional*

Whether to log the progress bar on a single line.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**xtol_abs** : *<class 'float'>, optional*

The absolute tolerance on the design parameters.


By default it is set to 1e-09.


.. raw:: html

    </li>

    <li>

**xtol_rel** : *<class 'float'>, optional*

The relative tolerance on the design parameters.


By default it is set to 1e-09.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _Augmented_Lagrangian_order_1_options:

Augmented_Lagrangian_order_1
----------------------------



Module: :class:`gemseo.algos.opt.augmented_lagrangian.augmented_lagrangian_order_1`


:code:`from gemseo.settings.opt import Augmented_Lagrangian_order_1_Settings`



Augmented Lagrangian algorithm using gradient information























































































































































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Required settings</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**sub_algorithm_name** : *<class 'str'>*

The name of the optimizer used to solve each sub-problem.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**enable_progress_bar** : *typing.Optional[bool], optional*

Whether to enable the progress bar in the optimization log.

If ``None``, use the global value of ``enable_progress_bar`` (see the
``configure`` function to change it globally).


By default it is set to None.


.. raw:: html

    </li>

    <li>

**eq_tolerance** : *<class 'float'>, optional*

The tolerance on the equality constraints.


By default it is set to 0.01.


.. raw:: html

    </li>

    <li>

**ftol_abs** : *<class 'float'>, optional*

The absolute tolerance on the objective function.


By default it is set to 1e-09.


.. raw:: html

    </li>

    <li>

**ftol_rel** : *<class 'float'>, optional*

The relative tolerance on the objective function.


By default it is set to 1e-09.


.. raw:: html

    </li>

    <li>

**gamma** : *<class 'float'>, optional*

The penalty increase factor.


By default it is set to 1.5.


.. raw:: html

    </li>

    <li>

**ineq_tolerance** : *<class 'float'>, optional*

The tolerance on the inequality constraints.


By default it is set to 0.0001.


.. raw:: html

    </li>

    <li>

**initial_rho** : *<class 'float'>, optional*

The initial penalty value.


By default it is set to 10.0.


.. raw:: html

    </li>

    <li>

**kkt_tol_abs** : *<class 'float'>, optional*

The absolute tolerance on the KKT residual norm.

If ``inf`` this criterion is not activated.


By default it is set to inf.


.. raw:: html

    </li>

    <li>

**kkt_tol_rel** : *<class 'float'>, optional*

The relative tolerance on the KKT residual norm.

If ``inf`` this criterion is not activated.


By default it is set to inf.


.. raw:: html

    </li>

    <li>

**log_problem** : *<class 'bool'>, optional*

Whether to log the definition and result of the problem.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**max_iter** : *<class 'int'>, optional*

The maximum number of iterations.


By default it is set to 1000.


.. raw:: html

    </li>

    <li>

**max_rho** : *<class 'float'>, optional*

The maximum penalty value.


By default it is set to 10000.


.. raw:: html

    </li>

    <li>

**max_time** : *<class 'float'>, optional*

The maximum runtime in seconds, disabled if 0.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**normalize_design_space** : *<class 'bool'>, optional*

Whether to normalize the design space variables between 0 and 1.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**reset_iteration_counters** : *<class 'bool'>, optional*

Whether to reset the iteration counters before each execution.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**round_ints** : *<class 'bool'>, optional*

Whether to round the integer variables.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**scaling_threshold** : *typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional*

The threshold on the reference function value that triggers scaling.

If ``None``, do not scale the functions.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**stop_crit_n_x** : *<class 'int'>, optional*

The minimum number of design vectors to consider in the stopping criteria.


By default it is set to 3.


.. raw:: html

    </li>

    <li>

**store_jacobian** : *<class 'bool'>, optional*

Whether to store the Jacobian matrices in the database.

This argument is ignored when the ``use_database`` option is ``False``.
If a gradient-based algorithm is used,
this option cannot be set along with kkt options.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**sub_algorithm_settings** : *collections.abc.Mapping[str, typing.Any], optional*

The settings of the optimizer used to solve each sub-problem.


By default it is set to {}.


.. raw:: html

    </li>

    <li>

**sub_problem_constraints** : *collections.abc.Iterable[str], optional*

The constraints to keep in the sub-problem.

If ``empty``, all constraints are handled by the Augmented Lagrangian method
which implies that the sub-problem is unconstrained.


By default it is set to ().


.. raw:: html

    </li>

    <li>

**tau** : *<class 'float'>, optional*

The threshold to increase the penalty.


By default it is set to 0.9.


.. raw:: html

    </li>

    <li>

**update_options_callback** : *typing.Optional[typing.Annotated[typing.Callable[[typing.Any], typing.Any], WithJsonSchema(json_schema={}, mode=None)]], optional*

A callable for updating parameters or a function call.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**use_database** : *<class 'bool'>, optional*

Whether to wrap the functions in the database.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_one_line_progress_bar** : *<class 'bool'>, optional*

Whether to log the progress bar on a single line.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**xtol_abs** : *<class 'float'>, optional*

The absolute tolerance on the design parameters.


By default it is set to 1e-09.


.. raw:: html

    </li>

    <li>

**xtol_rel** : *<class 'float'>, optional*

The relative tolerance on the design parameters.


By default it is set to 1e-09.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _DIFFERENTIAL_EVOLUTION_options:

DIFFERENTIAL_EVOLUTION
----------------------



Module: :class:`gemseo.algos.opt.scipy_global.scipy_global`


:code:`from gemseo.settings.opt import DIFFERENTIAL_EVOLUTION_Settings`



Differential Evolution algorithm



More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.differential_evolution.html.



































































































































































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**atol** : *<class 'float'>, optional*

The absolute tolerance for convergence.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**disp** : *<class 'bool'>, optional*

Whether to print convergence messages.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**enable_progress_bar** : *typing.Optional[bool], optional*

Whether to enable the progress bar in the optimization log.

If ``None``, use the global value of ``enable_progress_bar`` (see the
``configure`` function to change it globally).


By default it is set to None.


.. raw:: html

    </li>

    <li>

**eq_tolerance** : *<class 'float'>, optional*

The tolerance on the equality constraints.


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**ftol_abs** : *<class 'float'>, optional*

The absolute tolerance on the objective function.


By default it is set to 1e-09.


.. raw:: html

    </li>

    <li>

**ftol_rel** : *<class 'float'>, optional*

The relative tolerance on the objective function.


By default it is set to 1e-09.


.. raw:: html

    </li>

    <li>

**ineq_tolerance** : *<class 'float'>, optional*

The tolerance on the inequality constraints.


By default it is set to 0.0001.


.. raw:: html

    </li>

    <li>

**init** : *typing.Union[str, gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[float]]], optional*

The method to perform the population initialization as a string
         or the initial population as an array.


By default it is set to latinhypercube.


.. raw:: html

    </li>

    <li>

**log_problem** : *<class 'bool'>, optional*

Whether to log the definition and result of the problem.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**max_iter** : *<class 'int'>, optional*

The maximum number of iterations.


By default it is set to 9223372036854775807.


.. raw:: html

    </li>

    <li>

**max_time** : *<class 'float'>, optional*

The maximum runtime in seconds, disabled if 0.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**mutation** : *typing.Union[float, tuple[float, float]], optional*

The mutation constant.

If specified as a float it should be in the range [0, 2]. If specified as a
tuple(min, max) dithering is employed.


By default it is set to (0.5, 1.0).


.. raw:: html

    </li>

    <li>

**normalize_design_space** : *<class 'bool'>, optional*

Whether to normalize the design space variables between 0 and 1.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**polish** : *<class 'bool'>, optional*

Whether to polish the best population member at the end.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**popsize** : *<class 'int'>, optional*

The multiplier for setting the total population size.


By default it is set to 15.


.. raw:: html

    </li>

    <li>

**recombination** : *<class 'float'>, optional*

The recombination constant.


By default it is set to 0.7.


.. raw:: html

    </li>

    <li>

**reset_iteration_counters** : *<class 'bool'>, optional*

Whether to reset the iteration counters before each execution.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**round_ints** : *<class 'bool'>, optional*

Whether to round the integer variables.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**scaling_threshold** : *typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional*

The threshold on the reference function value that triggers scaling.

If ``None``, do not scale the functions.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**seed** : *<class 'int'>, optional*

The random seed.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**stop_crit_n_x** : *<class 'int'>, optional*

The minimum number of design vectors to consider in the stopping criteria.


By default it is set to 3.


.. raw:: html

    </li>

    <li>

**store_jacobian** : *<class 'bool'>, optional*

Whether to store the Jacobian matrices in the database.

This argument is ignored when the ``use_database`` option is ``False``.
If a gradient-based algorithm is used,
this option cannot be set along with kkt options.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**strategy** : *<class 'str'>, optional*

The differential evolution strategy to use.


By default it is set to best1bin.


.. raw:: html

    </li>

    <li>

**tol** : *<class 'float'>, optional*

The relative tolerance for convergence.


By default it is set to 0.01.


.. raw:: html

    </li>

    <li>

**updating** : *<class 'str'>, optional*

The best solution vector updating strategy.


By default it is set to immediate.


.. raw:: html

    </li>

    <li>

**use_database** : *<class 'bool'>, optional*

Whether to wrap the functions in the database.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_one_line_progress_bar** : *<class 'bool'>, optional*

Whether to log the progress bar on a single line.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**workers** : *<class 'int'>, optional*

The number of parallel workers the population is subdivided in.


By default it is set to 1.


.. raw:: html

    </li>

    <li>

**xtol_abs** : *<class 'float'>, optional*

The absolute tolerance on the design parameters.


By default it is set to 1e-09.


.. raw:: html

    </li>

    <li>

**xtol_rel** : *<class 'float'>, optional*

The relative tolerance on the design parameters.


By default it is set to 1e-09.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _DUAL_ANNEALING_options:

DUAL_ANNEALING
--------------



Module: :class:`gemseo.algos.opt.scipy_global.scipy_global`


:code:`from gemseo.settings.opt import DUAL_ANNEALING_Settings`



Dual annealing



More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.dual_annealing.html.































































































































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**accept** : *<class 'float'>, optional*

The acceptance distribution parameter.

The lower the acceptance parameter, the smaller the probability of acceptance.


By default it is set to -5.


.. raw:: html

    </li>

    <li>

**enable_progress_bar** : *typing.Optional[bool], optional*

Whether to enable the progress bar in the optimization log.

If ``None``, use the global value of ``enable_progress_bar`` (see the
``configure`` function to change it globally).


By default it is set to None.


.. raw:: html

    </li>

    <li>

**eq_tolerance** : *<class 'float'>, optional*

The tolerance on the equality constraints.


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**ftol_abs** : *<class 'float'>, optional*

The absolute tolerance on the objective function.


By default it is set to 1e-09.


.. raw:: html

    </li>

    <li>

**ftol_rel** : *<class 'float'>, optional*

The relative tolerance on the objective function.


By default it is set to 1e-09.


.. raw:: html

    </li>

    <li>

**ineq_tolerance** : *<class 'float'>, optional*

The tolerance on the inequality constraints.


By default it is set to 0.0001.


.. raw:: html

    </li>

    <li>

**initial_temp** : *<class 'float'>, optional*

The initial temperature.

Use higher values to facilitates a wider search of the energy landscape.


By default it is set to 5230.


.. raw:: html

    </li>

    <li>

**log_problem** : *<class 'bool'>, optional*

Whether to log the definition and result of the problem.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**max_iter** : *<class 'int'>, optional*

The maximum number of iterations.


By default it is set to 9223372036854775807.


.. raw:: html

    </li>

    <li>

**max_time** : *<class 'float'>, optional*

The maximum runtime in seconds, disabled if 0.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**no_local_search** : *<class 'bool'>, optional*

Whether to perform local search.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**normalize_design_space** : *<class 'bool'>, optional*

Whether to normalize the design space variables between 0 and 1.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**reset_iteration_counters** : *<class 'bool'>, optional*

Whether to reset the iteration counters before each execution.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**restart_temp_ratio** : *<class 'float'>, optional*

The temperature ratio under which the reannealing process is triggered.


By default it is set to 2e-05.


.. raw:: html

    </li>

    <li>

**round_ints** : *<class 'bool'>, optional*

Whether to round the integer variables.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**scaling_threshold** : *typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional*

The threshold on the reference function value that triggers scaling.

If ``None``, do not scale the functions.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**seed** : *<class 'int'>, optional*

The random seed.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**stop_crit_n_x** : *<class 'int'>, optional*

The minimum number of design vectors to consider in the stopping criteria.


By default it is set to 3.


.. raw:: html

    </li>

    <li>

**store_jacobian** : *<class 'bool'>, optional*

Whether to store the Jacobian matrices in the database.

This argument is ignored when the ``use_database`` option is ``False``.
If a gradient-based algorithm is used,
this option cannot be set along with kkt options.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_database** : *<class 'bool'>, optional*

Whether to wrap the functions in the database.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_one_line_progress_bar** : *<class 'bool'>, optional*

Whether to log the progress bar on a single line.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**visit** : *<class 'float'>, optional*

The visiting distribution parameter.

Higher values give the visiting distribution a heavier tail, this makes the
algorithm jump to a more distant region.


By default it is set to 2.62.


.. raw:: html

    </li>

    <li>

**xtol_abs** : *<class 'float'>, optional*

The absolute tolerance on the design parameters.


By default it is set to 1e-09.


.. raw:: html

    </li>

    <li>

**xtol_rel** : *<class 'float'>, optional*

The relative tolerance on the design parameters.


By default it is set to 1e-09.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _DUAL_SIMPLEX_options:

DUAL_SIMPLEX
------------



Module: :class:`gemseo.algos.opt.scipy_linprog.scipy_linprog`


:code:`from gemseo.settings.opt import DUAL_SIMPLEX_Settings`



Linear programming using the HiGHS dual simplex solver.



More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/optimize.linprog-highs-ds.html.











































































































































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**autoscale** : *<class 'bool'>, optional*

Whether to perform auto-scaling of the constraints.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**disp** : *<class 'bool'>, optional*

Whether to print convergence messages.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**dual_feasibility_tolerance** : *<class 'float'>, optional*

The dual feasability tolerance.


By default it is set to 1e-07.


.. raw:: html

    </li>

    <li>

**enable_progress_bar** : *typing.Optional[bool], optional*

Whether to enable the progress bar in the optimization log.

If ``None``, use the global value of ``enable_progress_bar`` (see the
``configure`` function to change it globally).


By default it is set to None.


.. raw:: html

    </li>

    <li>

**eq_tolerance** : *<class 'float'>, optional*

The tolerance on the equality constraints.


By default it is set to 0.01.


.. raw:: html

    </li>

    <li>

**ftol_abs** : *<class 'float'>, optional*

The absolute tolerance on the objective function.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**ftol_rel** : *<class 'float'>, optional*

The relative tolerance on the objective function.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**ineq_tolerance** : *<class 'float'>, optional*

The tolerance on the inequality constraints.


By default it is set to 0.0001.


.. raw:: html

    </li>

    <li>

**log_problem** : *<class 'bool'>, optional*

Whether to log the definition and result of the problem.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**max_iter** : *<class 'int'>, optional*

The maximum number of iterations.


By default it is set to 1000.


.. raw:: html

    </li>

    <li>

**max_time** : *<class 'float'>, optional*

The maximum runtime in seconds, disabled if 0.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**normalize_design_space** : *<class 'bool'>, optional*

Whether to normalize the design space variables between 0 and 1.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**presolve** : *<class 'bool'>, optional*

Whether to perform a preliminary analysis on the problem before solving.

It attempts to detect infeasibility, unboundedness or problem simplifications.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**primal_feasibility_tolerance** : *<class 'float'>, optional*

The primal feasability tolerance.


By default it is set to 1e-07.


.. raw:: html

    </li>

    <li>

**reset_iteration_counters** : *<class 'bool'>, optional*

Whether to reset the iteration counters before each execution.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**round_ints** : *<class 'bool'>, optional*

Whether to round the integer variables.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**rr** : *<class 'bool'>, optional*

Whether to remove linearly dependent equality-constraints.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**rr_method** : *typing.Literal['SVD', 'pivot', 'ID', None], optional*

The method to remove redundancy, either 'SVD', 'pivot' or 'ID'.

If ``None``, use “SVD” if the matrix is nearly full rank. If not, uses
“pivot”. The behavior of this default is subject to change without prior notice.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**scaling_threshold** : *typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional*

The threshold on the reference function value that triggers scaling.

If ``None``, do not scale the functions.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**simplex_dual_edge_weight_strategy** : *<class 'str'>, optional*

Strategy for simplex dual edge weights.

Available strategies: `dantzig`, `devex`, `steepest` and `steepest-devex`.



By default it is set to steepest-devex.


.. raw:: html

    </li>

    <li>

**stop_crit_n_x** : *<class 'int'>, optional*

The minimum number of design vectors to consider in the stopping criteria.


By default it is set to 3.


.. raw:: html

    </li>

    <li>

**store_jacobian** : *<class 'bool'>, optional*

Whether to store the Jacobian matrices in the database.

This argument is ignored when the ``use_database`` option is ``False``.
If a gradient-based algorithm is used,
this option cannot be set along with kkt options.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_database** : *<class 'bool'>, optional*

Whether to wrap the functions in the database.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_one_line_progress_bar** : *<class 'bool'>, optional*

Whether to log the progress bar on a single line.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**xtol_abs** : *<class 'float'>, optional*

The absolute tolerance on the design parameters.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**xtol_rel** : *<class 'float'>, optional*

The relative tolerance on the design parameters.


By default it is set to 0.0.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _INTERIOR_POINT_options:

INTERIOR_POINT
--------------



Module: :class:`gemseo.algos.opt.scipy_linprog.scipy_linprog`


:code:`from gemseo.settings.opt import INTERIOR_POINT_Settings`



Linear programming using the HiGHS interior point solver.



More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/optimize.linprog-highs-ipm.html.











































































































































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**autoscale** : *<class 'bool'>, optional*

Whether to perform auto-scaling of the constraints.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**disp** : *<class 'bool'>, optional*

Whether to print convergence messages.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**dual_feasibility_tolerance** : *<class 'float'>, optional*

The tolerance on the feasibility of the dual problem.


By default it is set to 1e-07.


.. raw:: html

    </li>

    <li>

**enable_progress_bar** : *typing.Optional[bool], optional*

Whether to enable the progress bar in the optimization log.

If ``None``, use the global value of ``enable_progress_bar`` (see the
``configure`` function to change it globally).


By default it is set to None.


.. raw:: html

    </li>

    <li>

**eq_tolerance** : *<class 'float'>, optional*

The tolerance on the equality constraints.


By default it is set to 0.01.


.. raw:: html

    </li>

    <li>

**ftol_abs** : *<class 'float'>, optional*

The absolute tolerance on the objective function.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**ftol_rel** : *<class 'float'>, optional*

The relative tolerance on the objective function.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**ineq_tolerance** : *<class 'float'>, optional*

The tolerance on the inequality constraints.


By default it is set to 0.0001.


.. raw:: html

    </li>

    <li>

**ipm_optimality_tolerance** : *<class 'float'>, optional*

Optimality tolerance.


By default it is set to 1e-08.


.. raw:: html

    </li>

    <li>

**log_problem** : *<class 'bool'>, optional*

Whether to log the definition and result of the problem.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**max_iter** : *<class 'int'>, optional*

The maximum number of iterations.


By default it is set to 1000.


.. raw:: html

    </li>

    <li>

**max_time** : *<class 'float'>, optional*

The maximum runtime in seconds, disabled if 0.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**normalize_design_space** : *<class 'bool'>, optional*

Whether to normalize the design space variables between 0 and 1.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**presolve** : *<class 'bool'>, optional*

Whether to perform a preliminary analysis on the problem before solving.

It attempts to detect infeasibility, unboundedness or problem simplifications.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**primal_feasibility_tolerance** : *<class 'float'>, optional*

The tolerance on the feasibility of the primal problem.


By default it is set to 1e-07.


.. raw:: html

    </li>

    <li>

**reset_iteration_counters** : *<class 'bool'>, optional*

Whether to reset the iteration counters before each execution.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**round_ints** : *<class 'bool'>, optional*

Whether to round the integer variables.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**rr** : *<class 'bool'>, optional*

Whether to remove linearly dependent equality-constraints.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**rr_method** : *typing.Literal['SVD', 'pivot', 'ID', None], optional*

The method to remove redundancy, either 'SVD', 'pivot' or 'ID'.

If ``None``, use “SVD” if the matrix is nearly full rank. If not, uses
“pivot”. The behavior of this default is subject to change without prior notice.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**scaling_threshold** : *typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional*

The threshold on the reference function value that triggers scaling.

If ``None``, do not scale the functions.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**stop_crit_n_x** : *<class 'int'>, optional*

The minimum number of design vectors to consider in the stopping criteria.


By default it is set to 3.


.. raw:: html

    </li>

    <li>

**store_jacobian** : *<class 'bool'>, optional*

Whether to store the Jacobian matrices in the database.

This argument is ignored when the ``use_database`` option is ``False``.
If a gradient-based algorithm is used,
this option cannot be set along with kkt options.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_database** : *<class 'bool'>, optional*

Whether to wrap the functions in the database.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_one_line_progress_bar** : *<class 'bool'>, optional*

Whether to log the progress bar on a single line.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**xtol_abs** : *<class 'float'>, optional*

The absolute tolerance on the design parameters.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**xtol_rel** : *<class 'float'>, optional*

The relative tolerance on the design parameters.


By default it is set to 0.0.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _L-BFGS-B_options:

L-BFGS-B
--------



Module: :class:`gemseo.algos.opt.scipy_local.scipy_local`


:code:`from gemseo.settings.opt import L_BFGS_B_Settings`



Limited-memory BFGS algorithm implemented in the SciPy library



More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/optimize.minimize-lbfgsb.html.





































































































































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**disp** : *<class 'bool'>, optional*

Whether to print convergence messages.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**enable_progress_bar** : *typing.Optional[bool], optional*

Whether to enable the progress bar in the optimization log.

If ``None``, use the global value of ``enable_progress_bar`` (see the
``configure`` function to change it globally).


By default it is set to None.


.. raw:: html

    </li>

    <li>

**eq_tolerance** : *<class 'float'>, optional*

The tolerance on the equality constraints.


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**ftol_abs** : *<class 'float'>, optional*

The absolute tolerance on the objective function.


By default it is set to 1e-09.


.. raw:: html

    </li>

    <li>

**ftol_rel** : *<class 'float'>, optional*

The relative tolerance on the objective function.


By default it is set to 1e-09.


.. raw:: html

    </li>

    <li>

**gtol** : *<class 'float'>, optional*

The precision goal for the projected gradient value to stop the algorithm.


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**ineq_tolerance** : *<class 'float'>, optional*

The tolerance on the inequality constraints.


By default it is set to 0.0001.


.. raw:: html

    </li>

    <li>

**iprint** : *<class 'int'>, optional*

The flag to control the frequency of output.

Default is no output.


By default it is set to -1.


.. raw:: html

    </li>

    <li>

**kkt_tol_abs** : *<class 'float'>, optional*

The absolute tolerance on the KKT residual norm.

If ``inf`` this criterion is not activated.


By default it is set to inf.


.. raw:: html

    </li>

    <li>

**kkt_tol_rel** : *<class 'float'>, optional*

The relative tolerance on the KKT residual norm.

If ``inf`` this criterion is not activated.


By default it is set to inf.


.. raw:: html

    </li>

    <li>

**log_problem** : *<class 'bool'>, optional*

Whether to log the definition and result of the problem.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**max_iter** : *<class 'int'>, optional*

The maximum number of iterations.


By default it is set to 1000.


.. raw:: html

    </li>

    <li>

**max_time** : *<class 'float'>, optional*

The maximum runtime in seconds, disabled if 0.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**maxcor** : *<class 'int'>, optional*

The maximum number of corrections for the limited memory matrix.


By default it is set to 20.


.. raw:: html

    </li>

    <li>

**maxls** : *<class 'int'>, optional*

The maximum number of line search steps per iteration.


By default it is set to 20.


.. raw:: html

    </li>

    <li>

**normalize_design_space** : *<class 'bool'>, optional*

Whether to normalize the design space variables between 0 and 1.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**reset_iteration_counters** : *<class 'bool'>, optional*

Whether to reset the iteration counters before each execution.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**round_ints** : *<class 'bool'>, optional*

Whether to round the integer variables.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**scaling_threshold** : *typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional*

The threshold on the reference function value that triggers scaling.

If ``None``, do not scale the functions.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**stop_crit_n_x** : *<class 'int'>, optional*

The minimum number of design vectors to consider in the stopping criteria.


By default it is set to 3.


.. raw:: html

    </li>

    <li>

**store_jacobian** : *<class 'bool'>, optional*

Whether to store the Jacobian matrices in the database.

This argument is ignored when the ``use_database`` option is ``False``.
If a gradient-based algorithm is used,
this option cannot be set along with kkt options.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_database** : *<class 'bool'>, optional*

Whether to wrap the functions in the database.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_one_line_progress_bar** : *<class 'bool'>, optional*

Whether to log the progress bar on a single line.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**xtol_abs** : *<class 'float'>, optional*

The absolute tolerance on the design parameters.


By default it is set to 1e-09.


.. raw:: html

    </li>

    <li>

**xtol_rel** : *<class 'float'>, optional*

The relative tolerance on the design parameters.


By default it is set to 1e-09.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _MNBI_options:

MNBI
----



Module: :class:`gemseo.algos.opt.mnbi.mnbi`


:code:`from gemseo.settings.opt import MNBI_Settings`



Modified Normal Boundary Intersection (mNBI) method



































































































































































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Required settings</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**sub_optim_algo** : *<class 'str'>*

The optimization algorithm used to solve the sub-optimization problems.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**custom_anchor_points** : *collections.abc.Sequence[gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[+_ScalarType_co]]], optional*

The bounding points of the custom phi simplex for the optimization.


By default it is set to ().


.. raw:: html

    </li>

    <li>

**custom_phi_betas** : *collections.abc.Sequence[gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[+_ScalarType_co]]], optional*

The custom values of :math:`\\Phi \beta` to be used in the optimization.


By default it is set to ().


.. raw:: html

    </li>

    <li>

**debug** : *<class 'bool'>, optional*

Whether to output the sub-optimization optima in a database hdf file.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**debug_file_path** : *typing.Union[str, pathlib.Path], optional*

The path to the debug file if debug mode is active.


By default it is set to debug_history.h5.


.. raw:: html

    </li>

    <li>

**doe_algo** : *<class 'str'>, optional*


            The design of experiments algo for the target points on the Pareto front.

A ``fullfactorial`` DOE is used default as these tend to be low dimensions,
usually not more than 3 objectives for a given problem.
This setting is relevant only for problems with more than 2 objectives.


By default it is set to PYDOE_FULLFACT.


.. raw:: html

    </li>

    <li>

**doe_algo_settings** : *collections.abc.Mapping[str, typing.Any], optional*

The settings for the DOE algorithm.


By default it is set to {}.


.. raw:: html

    </li>

    <li>

**enable_progress_bar** : *typing.Optional[bool], optional*

Whether to enable the progress bar in the optimization log.

If ``None``, use the global value of ``enable_progress_bar`` (see the
``configure`` function to change it globally).


By default it is set to None.


.. raw:: html

    </li>

    <li>

**eq_tolerance** : *<class 'float'>, optional*

The tolerance on the equality constraints.


By default it is set to 0.01.


.. raw:: html

    </li>

    <li>

**ftol_abs** : *<class 'float'>, optional*

The absolute tolerance on the objective function.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**ftol_rel** : *<class 'float'>, optional*

The relative tolerance on the objective function.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**ineq_tolerance** : *<class 'float'>, optional*

The tolerance on the inequality constraints.


By default it is set to 0.0001.


.. raw:: html

    </li>

    <li>

**log_problem** : *<class 'bool'>, optional*

Whether to log the definition and result of the problem.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**max_iter** : *<class 'int'>, optional*

The maximum number of iterations.


By default it is set to 1000.


.. raw:: html

    </li>

    <li>

**max_time** : *<class 'float'>, optional*

The maximum runtime in seconds, disabled if 0.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**n_processes** : *<class 'int'>, optional*

The maximum number of processes used to parallelize the sub-optimizations.


By default it is set to 1.


.. raw:: html

    </li>

    <li>

**n_sub_optim** : *<class 'int'>, optional*

The number of sub-optimizations points.

mNBI generates ``n_sub_optim`` points on the Pareto front between the
`n-objective` individual minima. This value must be strictly greater than
the number of objectives of the problem.


By default it is set to 1.


.. raw:: html

    </li>

    <li>

**normalize_design_space** : *<class 'bool'>, optional*

Whether to normalize the design space variables between 0 and 1.

The mNBI algorithm does not allow to normalize the design space at the top
level, only the sub-optimizations accept design space normalization. To do
this, pass the setting ``normalize_design_space`` to
``sub_optim_algo_settings``.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**reset_iteration_counters** : *<class 'bool'>, optional*

Whether to reset the iteration counters before each execution.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**round_ints** : *<class 'bool'>, optional*

Whether to round the integer variables.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**scaling_threshold** : *typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional*

The threshold on the reference function value that triggers scaling.

If ``None``, do not scale the functions.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**skip_betas** : *<class 'bool'>, optional*

Whether to skip the sub-optimizations of relevant.

The sub-optimizations are skipped if they correspond to values of beta for
which the theoretical result has already been found.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**stop_crit_n_x** : *<class 'int'>, optional*

The minimum number of design vectors to consider in the stopping criteria.


By default it is set to 3.


.. raw:: html

    </li>

    <li>

**store_jacobian** : *<class 'bool'>, optional*

Whether to store the Jacobian matrices in the database.

This argument is ignored when the ``use_database`` option is ``False``.
If a gradient-based algorithm is used,
this option cannot be set along with kkt options.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**sub_optim_algo_settings** : *collections.abc.Mapping[str, typing.Any], optional*

The settings for the sub optimization algorithm.


By default it is set to {}.


.. raw:: html

    </li>

    <li>

**sub_optim_max_iter** : *<class 'int'>, optional*

The maximum number of iterations of the sub-optimization algorithms.

If 0, the ``max_iter`` value is used.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**use_database** : *<class 'bool'>, optional*

Whether to wrap the functions in the database.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_one_line_progress_bar** : *<class 'bool'>, optional*

Whether to log the progress bar on a single line.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**xtol_abs** : *<class 'float'>, optional*

The absolute tolerance on the design parameters.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**xtol_rel** : *<class 'float'>, optional*

The relative tolerance on the design parameters.


By default it is set to 0.0.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _MultiStart_options:

MultiStart
----------



Module: :class:`gemseo.algos.opt.multi_start.multi_start`


:code:`from gemseo.settings.opt import MultiStart_Settings`



The optimization algorithm ``multistart`` generates starting points using a DOE algorithmand run a sub-optimization algorithm from each starting point.Depending on the sub-optimization algorithm,``multistart`` can handle integer design variables,equality and inequality constraintsas well as multi-objective functions.













































































































































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**doe_algo_name** : *<class 'str'>, optional*

The name of the DOE algorithm.

The DOE algorthm is used to generate the sub-optimizations starting points.


By default it is set to LHS.


.. raw:: html

    </li>

    <li>

**doe_algo_settings** : *collections.abc.Mapping[str, typing.Any], optional*

The settings of the DOE algorithm.


By default it is set to {}.


.. raw:: html

    </li>

    <li>

**enable_progress_bar** : *typing.Optional[bool], optional*

Whether to enable the progress bar in the optimization log.

If ``None``, use the global value of ``enable_progress_bar`` (see the
``configure`` function to change it globally).


By default it is set to None.


.. raw:: html

    </li>

    <li>

**eq_tolerance** : *<class 'float'>, optional*

The tolerance on the equality constraints.


By default it is set to 0.01.


.. raw:: html

    </li>

    <li>

**ftol_abs** : *<class 'float'>, optional*

The absolute tolerance on the objective function.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**ftol_rel** : *<class 'float'>, optional*

The relative tolerance on the objective function.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**ineq_tolerance** : *<class 'float'>, optional*

The tolerance on the inequality constraints.


By default it is set to 0.0001.


.. raw:: html

    </li>

    <li>

**log_problem** : *<class 'bool'>, optional*

Whether to log the definition and result of the problem.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**max_iter** : *<class 'int'>, optional*

The maximum number of iterations.


By default it is set to 1000.


.. raw:: html

    </li>

    <li>

**max_time** : *<class 'float'>, optional*

The maximum runtime in seconds, disabled if 0.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**multistart_file_path** : *typing.Union[str, pathlib.Path]*

The database file path to save the local optima.

If empty, do not save the local optima.


By default it is set to .


.. raw:: html

    </li>

    <li>

**n_processes** : *<class 'int'>, optional*

The maximum number of processes used to parallelize the sub-optimizations.


By default it is set to 1.


.. raw:: html

    </li>

    <li>

**n_start** : *<class 'int'>, optional*

The number of sub-optimizations.


By default it is set to 5.


.. raw:: html

    </li>

    <li>

**normalize_design_space** : *<class 'bool'>, optional*

Whether to normalize the design space variables between 0 and 1.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**opt_algo_max_iter** : *<class 'int'>, optional*

The maximum number of iterations for each sub-optimization.

If 0, this number is ``int(max_iter/n_start)``.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**opt_algo_name** : *<class 'str'>, optional*

The name of the sub-optimization algorithm.


By default it is set to SLSQP.


.. raw:: html

    </li>

    <li>

**opt_algo_settings** : *collections.abc.Mapping[str, typing.Any], optional*

The settings of the sub-optimization algorithm.


By default it is set to {}.


.. raw:: html

    </li>

    <li>

**reset_iteration_counters** : *<class 'bool'>, optional*

Whether to reset the iteration counters before each execution.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**round_ints** : *<class 'bool'>, optional*

Whether to round the integer variables.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**scaling_threshold** : *typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional*

The threshold on the reference function value that triggers scaling.

If ``None``, do not scale the functions.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**stop_crit_n_x** : *<class 'int'>, optional*

The minimum number of design vectors to consider in the stopping criteria.


By default it is set to 3.


.. raw:: html

    </li>

    <li>

**store_jacobian** : *<class 'bool'>, optional*

Whether to store the Jacobian matrices in the database.

This argument is ignored when the ``use_database`` option is ``False``.
If a gradient-based algorithm is used,
this option cannot be set along with kkt options.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_database** : *<class 'bool'>, optional*

Whether to wrap the functions in the database.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_one_line_progress_bar** : *<class 'bool'>, optional*

Whether to log the progress bar on a single line.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**xtol_abs** : *<class 'float'>, optional*

The absolute tolerance on the design parameters.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**xtol_rel** : *<class 'float'>, optional*

The relative tolerance on the design parameters.


By default it is set to 0.0.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _NELDER-MEAD_options:

NELDER-MEAD
-----------



Module: :class:`gemseo.algos.opt.scipy_local.scipy_local`


:code:`from gemseo.settings.opt import NELDER_MEAD_Settings`



Nelder-Mead algorithm implemented in the SciPy library



More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/optimize.minimize-neldermead.html.



















































































































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**adaptive** : *<class 'bool'>, optional*

Whether to adapt the algorithm parameters to dimensionality of problem.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**disp** : *<class 'bool'>, optional*

Whether to print convergence messages.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**enable_progress_bar** : *typing.Optional[bool], optional*

Whether to enable the progress bar in the optimization log.

If ``None``, use the global value of ``enable_progress_bar`` (see the
``configure`` function to change it globally).


By default it is set to None.


.. raw:: html

    </li>

    <li>

**eq_tolerance** : *<class 'float'>, optional*

The tolerance on the equality constraints.


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**ftol_abs** : *<class 'float'>, optional*

The absolute tolerance on the objective function.


By default it is set to 1e-09.


.. raw:: html

    </li>

    <li>

**ftol_rel** : *<class 'float'>, optional*

The relative tolerance on the objective function.


By default it is set to 1e-09.


.. raw:: html

    </li>

    <li>

**ineq_tolerance** : *<class 'float'>, optional*

The tolerance on the inequality constraints.


By default it is set to 0.0001.


.. raw:: html

    </li>

    <li>

**initial_simplex** : *typing.Union[collections.abc.Sequence[float], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[float]], NoneType], optional*

The initial simplex.

If provided, the expected shape is `(N+1, N)` where `N` is the problem dimension.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**log_problem** : *<class 'bool'>, optional*

Whether to log the definition and result of the problem.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**max_iter** : *<class 'int'>, optional*

The maximum number of iterations.


By default it is set to 1000.


.. raw:: html

    </li>

    <li>

**max_time** : *<class 'float'>, optional*

The maximum runtime in seconds, disabled if 0.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**normalize_design_space** : *<class 'bool'>, optional*

Whether to normalize the design space variables between 0 and 1.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**reset_iteration_counters** : *<class 'bool'>, optional*

Whether to reset the iteration counters before each execution.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**return_all** : *<class 'bool'>, optional*

Whether to return a list of the best solution at each of the iterations.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**round_ints** : *<class 'bool'>, optional*

Whether to round the integer variables.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**scaling_threshold** : *typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional*

The threshold on the reference function value that triggers scaling.

If ``None``, do not scale the functions.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**stop_crit_n_x** : *<class 'int'>, optional*

The minimum number of design vectors to consider in the stopping criteria.


By default it is set to 3.


.. raw:: html

    </li>

    <li>

**store_jacobian** : *<class 'bool'>, optional*

Whether to store the Jacobian matrices in the database.

This argument is ignored when the ``use_database`` option is ``False``.
If a gradient-based algorithm is used,
this option cannot be set along with kkt options.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_database** : *<class 'bool'>, optional*

Whether to wrap the functions in the database.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_one_line_progress_bar** : *<class 'bool'>, optional*

Whether to log the progress bar on a single line.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**xtol_abs** : *<class 'float'>, optional*

The absolute tolerance on the design parameters.


By default it is set to 1e-09.


.. raw:: html

    </li>

    <li>

**xtol_rel** : *<class 'float'>, optional*

The relative tolerance on the design parameters.


By default it is set to 1e-09.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _NLOPT_BFGS_options:

NLOPT_BFGS
----------



Module: :class:`gemseo.algos.opt.nlopt.nlopt`


:code:`from gemseo.settings.opt import NLOPT_BFGS_Settings`



Broyden-Fletcher-Goldfarb-Shanno method (BFGS) implemented in the NLOPT library



More details about the algorithm and its settings on https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/#low-storage-bfgs.













































































































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**enable_progress_bar** : *typing.Optional[bool], optional*

Whether to enable the progress bar in the optimization log.

If ``None``, use the global value of ``enable_progress_bar`` (see the
``configure`` function to change it globally).


By default it is set to None.


.. raw:: html

    </li>

    <li>

**eq_tolerance** : *<class 'float'>, optional*

The tolerance on the equality constraints.


By default it is set to 0.01.


.. raw:: html

    </li>

    <li>

**ftol_abs** : *<class 'float'>, optional*

The absolute tolerance on the objective function.


By default it is set to 1e-14.


.. raw:: html

    </li>

    <li>

**ftol_rel** : *<class 'float'>, optional*

The relative tolerance on the objective function.


By default it is set to 1e-08.


.. raw:: html

    </li>

    <li>

**ineq_tolerance** : *<class 'float'>, optional*

The tolerance on the inequality constraints.


By default it is set to 0.0001.


.. raw:: html

    </li>

    <li>

**kkt_tol_abs** : *<class 'float'>, optional*

The absolute tolerance on the KKT residual norm.

If ``inf`` this criterion is not activated.


By default it is set to inf.


.. raw:: html

    </li>

    <li>

**kkt_tol_rel** : *<class 'float'>, optional*

The relative tolerance on the KKT residual norm.

If ``inf`` this criterion is not activated.


By default it is set to inf.


.. raw:: html

    </li>

    <li>

**log_problem** : *<class 'bool'>, optional*

Whether to log the definition and result of the problem.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**max_iter** : *<class 'int'>, optional*

The maximum number of iterations.


By default it is set to 1000.


.. raw:: html

    </li>

    <li>

**max_time** : *<class 'float'>, optional*

The maximum runtime in seconds, disabled if 0.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**normalize_design_space** : *<class 'bool'>, optional*

Whether to normalize the design space variables between 0 and 1.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**reset_iteration_counters** : *<class 'bool'>, optional*

Whether to reset the iteration counters before each execution.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**round_ints** : *<class 'bool'>, optional*

Whether to round the integer variables.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**scaling_threshold** : *typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional*

The threshold on the reference function value that triggers scaling.

If ``None``, do not scale the functions.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**stop_crit_n_x** : *typing.Optional[int], optional*

The minimum number of design vectors to consider in the stopping criteria.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**stopval** : *<class 'float'>, optional*

The objective value at which the optimization will stop.


By default it is set to -inf.


.. raw:: html

    </li>

    <li>

**store_jacobian** : *<class 'bool'>, optional*

Whether to store the Jacobian matrices in the database.

This argument is ignored when the ``use_database`` option is ``False``.
If a gradient-based algorithm is used,
this option cannot be set along with kkt options.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_database** : *<class 'bool'>, optional*

Whether to wrap the functions in the database.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_one_line_progress_bar** : *<class 'bool'>, optional*

Whether to log the progress bar on a single line.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**xtol_abs** : *<class 'float'>, optional*

The absolute tolerance on the design parameters.


By default it is set to 1e-14.


.. raw:: html

    </li>

    <li>

**xtol_rel** : *<class 'float'>, optional*

The relative tolerance on the design parameters.


By default it is set to 1e-08.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _NLOPT_BOBYQA_options:

NLOPT_BOBYQA
------------



Module: :class:`gemseo.algos.opt.nlopt.nlopt`


:code:`from gemseo.settings.opt import NLOPT_BOBYQA_Settings`



Bound Optimization BY Quadratic Approximation (BOBYQA) implemented in the NLOPT library



More details about the algorithm and its settings on https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/#bobyqa.







































































































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**enable_progress_bar** : *typing.Optional[bool], optional*

Whether to enable the progress bar in the optimization log.

If ``None``, use the global value of ``enable_progress_bar`` (see the
``configure`` function to change it globally).


By default it is set to None.


.. raw:: html

    </li>

    <li>

**eq_tolerance** : *<class 'float'>, optional*

The tolerance on the equality constraints.


By default it is set to 0.01.


.. raw:: html

    </li>

    <li>

**ftol_abs** : *<class 'float'>, optional*

The absolute tolerance on the objective function.


By default it is set to 1e-14.


.. raw:: html

    </li>

    <li>

**ftol_rel** : *<class 'float'>, optional*

The relative tolerance on the objective function.


By default it is set to 1e-08.


.. raw:: html

    </li>

    <li>

**ineq_tolerance** : *<class 'float'>, optional*

The tolerance on the inequality constraints.


By default it is set to 0.0001.


.. raw:: html

    </li>

    <li>

**init_step** : *typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional*

The initial step size for derivative-free algorithms.

It can be an array of the initial steps for each dimension, or a single
number if the same step will be used for all of them.

For derivative-free local-optimization algorithms, the optimizer must
somehow decide on some initial step size to perturb `x` by when it begins
the optimization. This step size should be big enough so that the value of
the objective significantly changes, but not too big if you want to find the
local optimum nearest to x.


By default it is set to 0.25.


.. raw:: html

    </li>

    <li>

**log_problem** : *<class 'bool'>, optional*

Whether to log the definition and result of the problem.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**max_iter** : *<class 'int'>, optional*

The maximum number of iterations.


By default it is set to 1000.


.. raw:: html

    </li>

    <li>

**max_time** : *<class 'float'>, optional*

The maximum runtime in seconds, disabled if 0.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**normalize_design_space** : *<class 'bool'>, optional*

Whether to normalize the design space variables between 0 and 1.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**reset_iteration_counters** : *<class 'bool'>, optional*

Whether to reset the iteration counters before each execution.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**round_ints** : *<class 'bool'>, optional*

Whether to round the integer variables.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**scaling_threshold** : *typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional*

The threshold on the reference function value that triggers scaling.

If ``None``, do not scale the functions.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**stop_crit_n_x** : *typing.Optional[int], optional*

The minimum number of design vectors to consider in the stopping criteria.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**stopval** : *<class 'float'>, optional*

The objective value at which the optimization will stop.


By default it is set to -inf.


.. raw:: html

    </li>

    <li>

**store_jacobian** : *<class 'bool'>, optional*

Whether to store the Jacobian matrices in the database.

This argument is ignored when the ``use_database`` option is ``False``.
If a gradient-based algorithm is used,
this option cannot be set along with kkt options.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_database** : *<class 'bool'>, optional*

Whether to wrap the functions in the database.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_one_line_progress_bar** : *<class 'bool'>, optional*

Whether to log the progress bar on a single line.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**xtol_abs** : *<class 'float'>, optional*

The absolute tolerance on the design parameters.


By default it is set to 1e-14.


.. raw:: html

    </li>

    <li>

**xtol_rel** : *<class 'float'>, optional*

The relative tolerance on the design parameters.


By default it is set to 1e-08.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _NLOPT_COBYLA_options:

NLOPT_COBYLA
------------



Module: :class:`gemseo.algos.opt.nlopt.nlopt`


:code:`from gemseo.settings.opt import NLOPT_COBYLA_Settings`



Constrained Optimization BY Linear Approximations (COBYLA) implemented in the NLOPT library



More details about the algorithm and its settings on https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/#cobyla-constrained-optimization-by-linear-approximations.







































































































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**enable_progress_bar** : *typing.Optional[bool], optional*

Whether to enable the progress bar in the optimization log.

If ``None``, use the global value of ``enable_progress_bar`` (see the
``configure`` function to change it globally).


By default it is set to None.


.. raw:: html

    </li>

    <li>

**eq_tolerance** : *<class 'float'>, optional*

The tolerance on the equality constraints.


By default it is set to 0.01.


.. raw:: html

    </li>

    <li>

**ftol_abs** : *<class 'float'>, optional*

The absolute tolerance on the objective function.


By default it is set to 1e-14.


.. raw:: html

    </li>

    <li>

**ftol_rel** : *<class 'float'>, optional*

The relative tolerance on the objective function.


By default it is set to 1e-08.


.. raw:: html

    </li>

    <li>

**ineq_tolerance** : *<class 'float'>, optional*

The tolerance on the inequality constraints.


By default it is set to 0.0001.


.. raw:: html

    </li>

    <li>

**init_step** : *typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional*

The initial step size for derivative-free algorithms.

It can be an array of the initial steps for each dimension, or a single
number if the same step will be used for all of them.

For derivative-free local-optimization algorithms, the optimizer must
somehow decide on some initial step size to perturb `x` by when it begins
the optimization. This step size should be big enough so that the value of
the objective significantly changes, but not too big if you want to find the
local optimum nearest to x.


By default it is set to 0.25.


.. raw:: html

    </li>

    <li>

**log_problem** : *<class 'bool'>, optional*

Whether to log the definition and result of the problem.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**max_iter** : *<class 'int'>, optional*

The maximum number of iterations.


By default it is set to 1000.


.. raw:: html

    </li>

    <li>

**max_time** : *<class 'float'>, optional*

The maximum runtime in seconds, disabled if 0.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**normalize_design_space** : *<class 'bool'>, optional*

Whether to normalize the design space variables between 0 and 1.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**reset_iteration_counters** : *<class 'bool'>, optional*

Whether to reset the iteration counters before each execution.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**round_ints** : *<class 'bool'>, optional*

Whether to round the integer variables.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**scaling_threshold** : *typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional*

The threshold on the reference function value that triggers scaling.

If ``None``, do not scale the functions.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**stop_crit_n_x** : *typing.Optional[int], optional*

The minimum number of design vectors to consider in the stopping criteria.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**stopval** : *<class 'float'>, optional*

The objective value at which the optimization will stop.


By default it is set to -inf.


.. raw:: html

    </li>

    <li>

**store_jacobian** : *<class 'bool'>, optional*

Whether to store the Jacobian matrices in the database.

This argument is ignored when the ``use_database`` option is ``False``.
If a gradient-based algorithm is used,
this option cannot be set along with kkt options.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_database** : *<class 'bool'>, optional*

Whether to wrap the functions in the database.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_one_line_progress_bar** : *<class 'bool'>, optional*

Whether to log the progress bar on a single line.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**xtol_abs** : *<class 'float'>, optional*

The absolute tolerance on the design parameters.


By default it is set to 1e-14.


.. raw:: html

    </li>

    <li>

**xtol_rel** : *<class 'float'>, optional*

The relative tolerance on the design parameters.


By default it is set to 1e-08.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _NLOPT_MMA_options:

NLOPT_MMA
---------



Module: :class:`gemseo.algos.opt.nlopt.nlopt`


:code:`from gemseo.settings.opt import NLOPT_MMA_Settings`



Method of Moving Asymptotes (MMA)implemented in the NLOPT library



More details about the algorithm and its settings on https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/#mma-method-of-moving-asymptotes-and-ccsa.



















































































































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**enable_progress_bar** : *typing.Optional[bool], optional*

Whether to enable the progress bar in the optimization log.

If ``None``, use the global value of ``enable_progress_bar`` (see the
``configure`` function to change it globally).


By default it is set to None.


.. raw:: html

    </li>

    <li>

**eq_tolerance** : *<class 'float'>, optional*

The tolerance on the equality constraints.


By default it is set to 0.01.


.. raw:: html

    </li>

    <li>

**ftol_abs** : *<class 'float'>, optional*

The absolute tolerance on the objective function.


By default it is set to 1e-14.


.. raw:: html

    </li>

    <li>

**ftol_rel** : *<class 'float'>, optional*

The relative tolerance on the objective function.


By default it is set to 1e-08.


.. raw:: html

    </li>

    <li>

**ineq_tolerance** : *<class 'float'>, optional*

The tolerance on the inequality constraints.


By default it is set to 0.0001.


.. raw:: html

    </li>

    <li>

**inner_maxeval** : *<class 'int'>, optional*

The maximum number of inner iterations of the algorithm.

The value 0 means that there is no limit.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**kkt_tol_abs** : *<class 'float'>, optional*

The absolute tolerance on the KKT residual norm.

If ``inf`` this criterion is not activated.


By default it is set to inf.


.. raw:: html

    </li>

    <li>

**kkt_tol_rel** : *<class 'float'>, optional*

The relative tolerance on the KKT residual norm.

If ``inf`` this criterion is not activated.


By default it is set to inf.


.. raw:: html

    </li>

    <li>

**log_problem** : *<class 'bool'>, optional*

Whether to log the definition and result of the problem.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**max_iter** : *<class 'int'>, optional*

The maximum number of iterations.


By default it is set to 1000.


.. raw:: html

    </li>

    <li>

**max_time** : *<class 'float'>, optional*

The maximum runtime in seconds, disabled if 0.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**normalize_design_space** : *<class 'bool'>, optional*

Whether to normalize the design space variables between 0 and 1.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**reset_iteration_counters** : *<class 'bool'>, optional*

Whether to reset the iteration counters before each execution.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**round_ints** : *<class 'bool'>, optional*

Whether to round the integer variables.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**scaling_threshold** : *typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional*

The threshold on the reference function value that triggers scaling.

If ``None``, do not scale the functions.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**stop_crit_n_x** : *typing.Optional[int], optional*

The minimum number of design vectors to consider in the stopping criteria.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**stopval** : *<class 'float'>, optional*

The objective value at which the optimization will stop.


By default it is set to -inf.


.. raw:: html

    </li>

    <li>

**store_jacobian** : *<class 'bool'>, optional*

Whether to store the Jacobian matrices in the database.

This argument is ignored when the ``use_database`` option is ``False``.
If a gradient-based algorithm is used,
this option cannot be set along with kkt options.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_database** : *<class 'bool'>, optional*

Whether to wrap the functions in the database.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_one_line_progress_bar** : *<class 'bool'>, optional*

Whether to log the progress bar on a single line.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**xtol_abs** : *<class 'float'>, optional*

The absolute tolerance on the design parameters.


By default it is set to 1e-14.


.. raw:: html

    </li>

    <li>

**xtol_rel** : *<class 'float'>, optional*

The relative tolerance on the design parameters.


By default it is set to 1e-08.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _NLOPT_NEWUOA_options:

NLOPT_NEWUOA
------------



Module: :class:`gemseo.algos.opt.nlopt.nlopt`


:code:`from gemseo.settings.opt import NLOPT_NEWUOA_Settings`



NEWUOA + bound constraints implemented in the NLOPT library



More details about the algorithm and its settings on https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/#newuoa-bound-constraints.







































































































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**enable_progress_bar** : *typing.Optional[bool], optional*

Whether to enable the progress bar in the optimization log.

If ``None``, use the global value of ``enable_progress_bar`` (see the
``configure`` function to change it globally).


By default it is set to None.


.. raw:: html

    </li>

    <li>

**eq_tolerance** : *<class 'float'>, optional*

The tolerance on the equality constraints.


By default it is set to 0.01.


.. raw:: html

    </li>

    <li>

**ftol_abs** : *<class 'float'>, optional*

The absolute tolerance on the objective function.


By default it is set to 1e-14.


.. raw:: html

    </li>

    <li>

**ftol_rel** : *<class 'float'>, optional*

The relative tolerance on the objective function.


By default it is set to 1e-08.


.. raw:: html

    </li>

    <li>

**ineq_tolerance** : *<class 'float'>, optional*

The tolerance on the inequality constraints.


By default it is set to 0.0001.


.. raw:: html

    </li>

    <li>

**init_step** : *typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional*

The initial step size for derivative-free algorithms.

It can be an array of the initial steps for each dimension, or a single
number if the same step will be used for all of them.

For derivative-free local-optimization algorithms, the optimizer must
somehow decide on some initial step size to perturb `x` by when it begins
the optimization. This step size should be big enough so that the value of
the objective significantly changes, but not too big if you want to find the
local optimum nearest to x.


By default it is set to 0.25.


.. raw:: html

    </li>

    <li>

**log_problem** : *<class 'bool'>, optional*

Whether to log the definition and result of the problem.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**max_iter** : *<class 'int'>, optional*

The maximum number of iterations.


By default it is set to 1000.


.. raw:: html

    </li>

    <li>

**max_time** : *<class 'float'>, optional*

The maximum runtime in seconds, disabled if 0.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**normalize_design_space** : *<class 'bool'>, optional*

Whether to normalize the design space variables between 0 and 1.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**reset_iteration_counters** : *<class 'bool'>, optional*

Whether to reset the iteration counters before each execution.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**round_ints** : *<class 'bool'>, optional*

Whether to round the integer variables.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**scaling_threshold** : *typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional*

The threshold on the reference function value that triggers scaling.

If ``None``, do not scale the functions.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**stop_crit_n_x** : *typing.Optional[int], optional*

The minimum number of design vectors to consider in the stopping criteria.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**stopval** : *<class 'float'>, optional*

The objective value at which the optimization will stop.


By default it is set to -inf.


.. raw:: html

    </li>

    <li>

**store_jacobian** : *<class 'bool'>, optional*

Whether to store the Jacobian matrices in the database.

This argument is ignored when the ``use_database`` option is ``False``.
If a gradient-based algorithm is used,
this option cannot be set along with kkt options.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_database** : *<class 'bool'>, optional*

Whether to wrap the functions in the database.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_one_line_progress_bar** : *<class 'bool'>, optional*

Whether to log the progress bar on a single line.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**xtol_abs** : *<class 'float'>, optional*

The absolute tolerance on the design parameters.


By default it is set to 1e-14.


.. raw:: html

    </li>

    <li>

**xtol_rel** : *<class 'float'>, optional*

The relative tolerance on the design parameters.


By default it is set to 1e-08.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _NLOPT_SLSQP_options:

NLOPT_SLSQP
-----------



Module: :class:`gemseo.algos.opt.nlopt.nlopt`


:code:`from gemseo.settings.opt import NLOPT_SLSQP_Settings`



Sequential Least-Squares Quadratic Programming (SLSQP) implemented in the NLOPT library



More details about the algorithm and its settings on https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/#slsqp.













































































































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**enable_progress_bar** : *typing.Optional[bool], optional*

Whether to enable the progress bar in the optimization log.

If ``None``, use the global value of ``enable_progress_bar`` (see the
``configure`` function to change it globally).


By default it is set to None.


.. raw:: html

    </li>

    <li>

**eq_tolerance** : *<class 'float'>, optional*

The tolerance on the equality constraints.


By default it is set to 0.01.


.. raw:: html

    </li>

    <li>

**ftol_abs** : *<class 'float'>, optional*

The absolute tolerance on the objective function.


By default it is set to 1e-14.


.. raw:: html

    </li>

    <li>

**ftol_rel** : *<class 'float'>, optional*

The relative tolerance on the objective function.


By default it is set to 1e-08.


.. raw:: html

    </li>

    <li>

**ineq_tolerance** : *<class 'float'>, optional*

The tolerance on the inequality constraints.


By default it is set to 0.0001.


.. raw:: html

    </li>

    <li>

**kkt_tol_abs** : *<class 'float'>, optional*

The absolute tolerance on the KKT residual norm.

If ``inf`` this criterion is not activated.


By default it is set to inf.


.. raw:: html

    </li>

    <li>

**kkt_tol_rel** : *<class 'float'>, optional*

The relative tolerance on the KKT residual norm.

If ``inf`` this criterion is not activated.


By default it is set to inf.


.. raw:: html

    </li>

    <li>

**log_problem** : *<class 'bool'>, optional*

Whether to log the definition and result of the problem.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**max_iter** : *<class 'int'>, optional*

The maximum number of iterations.


By default it is set to 1000.


.. raw:: html

    </li>

    <li>

**max_time** : *<class 'float'>, optional*

The maximum runtime in seconds, disabled if 0.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**normalize_design_space** : *<class 'bool'>, optional*

Whether to normalize the design space variables between 0 and 1.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**reset_iteration_counters** : *<class 'bool'>, optional*

Whether to reset the iteration counters before each execution.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**round_ints** : *<class 'bool'>, optional*

Whether to round the integer variables.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**scaling_threshold** : *typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional*

The threshold on the reference function value that triggers scaling.

If ``None``, do not scale the functions.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**stop_crit_n_x** : *typing.Optional[int], optional*

The minimum number of design vectors to consider in the stopping criteria.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**stopval** : *<class 'float'>, optional*

The objective value at which the optimization will stop.


By default it is set to -inf.


.. raw:: html

    </li>

    <li>

**store_jacobian** : *<class 'bool'>, optional*

Whether to store the Jacobian matrices in the database.

This argument is ignored when the ``use_database`` option is ``False``.
If a gradient-based algorithm is used,
this option cannot be set along with kkt options.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_database** : *<class 'bool'>, optional*

Whether to wrap the functions in the database.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_one_line_progress_bar** : *<class 'bool'>, optional*

Whether to log the progress bar on a single line.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**xtol_abs** : *<class 'float'>, optional*

The absolute tolerance on the design parameters.


By default it is set to 1e-14.


.. raw:: html

    </li>

    <li>

**xtol_rel** : *<class 'float'>, optional*

The relative tolerance on the design parameters.


By default it is set to 1e-08.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _SHGO_options:

SHGO
----



Module: :class:`gemseo.algos.opt.scipy_global.scipy_global`


:code:`from gemseo.settings.opt import SHGO_Settings`



Simplicial homology global optimization



More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.shgo.html.

























































































































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**enable_progress_bar** : *typing.Optional[bool], optional*

Whether to enable the progress bar in the optimization log.

If ``None``, use the global value of ``enable_progress_bar`` (see the
``configure`` function to change it globally).


By default it is set to None.


.. raw:: html

    </li>

    <li>

**eq_tolerance** : *<class 'float'>, optional*

The tolerance on the equality constraints.


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**ftol_abs** : *<class 'float'>, optional*

The absolute tolerance on the objective function.


By default it is set to 1e-09.


.. raw:: html

    </li>

    <li>

**ftol_rel** : *<class 'float'>, optional*

The relative tolerance on the objective function.


By default it is set to 1e-09.


.. raw:: html

    </li>

    <li>

**ineq_tolerance** : *<class 'float'>, optional*

The tolerance on the inequality constraints.


By default it is set to 0.0001.


.. raw:: html

    </li>

    <li>

**iters** : *<class 'int'>, optional*

The number of iterations used to construct the simplicial complex.


By default it is set to 1.


.. raw:: html

    </li>

    <li>

**log_problem** : *<class 'bool'>, optional*

Whether to log the definition and result of the problem.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**max_iter** : *<class 'int'>, optional*

The maximum number of iterations.


By default it is set to 9223372036854775807.


.. raw:: html

    </li>

    <li>

**max_time** : *<class 'float'>, optional*

The maximum runtime in seconds, disabled if 0.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**n** : *<class 'int'>, optional*

The number of samples used to construct the simplicial complex.


By default it is set to 100.


.. raw:: html

    </li>

    <li>

**normalize_design_space** : *<class 'bool'>, optional*

Whether to normalize the design space variables between 0 and 1.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**options** : *collections.abc.Mapping[str, typing.Any], optional*

The options for the local optimization algorithm.


By default it is set to {}.


.. raw:: html

    </li>

    <li>

**reset_iteration_counters** : *<class 'bool'>, optional*

Whether to reset the iteration counters before each execution.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**round_ints** : *<class 'bool'>, optional*

Whether to round the integer variables.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**sampling_method** : *<class 'str'>, optional*

The sampling method.


By default it is set to simplicial.


.. raw:: html

    </li>

    <li>

**scaling_threshold** : *typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional*

The threshold on the reference function value that triggers scaling.

If ``None``, do not scale the functions.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**stop_crit_n_x** : *<class 'int'>, optional*

The minimum number of design vectors to consider in the stopping criteria.


By default it is set to 3.


.. raw:: html

    </li>

    <li>

**store_jacobian** : *<class 'bool'>, optional*

Whether to store the Jacobian matrices in the database.

This argument is ignored when the ``use_database`` option is ``False``.
If a gradient-based algorithm is used,
this option cannot be set along with kkt options.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_database** : *<class 'bool'>, optional*

Whether to wrap the functions in the database.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_one_line_progress_bar** : *<class 'bool'>, optional*

Whether to log the progress bar on a single line.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**workers** : *<class 'int'>, optional*

The number workers to parallelize on.


By default it is set to 1.


.. raw:: html

    </li>

    <li>

**xtol_abs** : *<class 'float'>, optional*

The absolute tolerance on the design parameters.


By default it is set to 1e-09.


.. raw:: html

    </li>

    <li>

**xtol_rel** : *<class 'float'>, optional*

The relative tolerance on the design parameters.


By default it is set to 1e-09.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _SLSQP_options:

SLSQP
-----



Module: :class:`gemseo.algos.opt.scipy_local.scipy_local`


:code:`from gemseo.settings.opt import SLSQP_Settings`



Sequential Least-Squares Quadratic Programming (SLSQP) implemented in the SciPy library



More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/optimize.minimize-slsqp.html.



















































































































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**disp** : *<class 'bool'>, optional*

Whether to print convergence messages.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**enable_progress_bar** : *typing.Optional[bool], optional*

Whether to enable the progress bar in the optimization log.

If ``None``, use the global value of ``enable_progress_bar`` (see the
``configure`` function to change it globally).


By default it is set to None.


.. raw:: html

    </li>

    <li>

**eq_tolerance** : *<class 'float'>, optional*

The tolerance on the equality constraints.


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**ftol_abs** : *<class 'float'>, optional*

The absolute tolerance on the objective function.


By default it is set to 1e-09.


.. raw:: html

    </li>

    <li>

**ftol_rel** : *<class 'float'>, optional*

The relative tolerance on the objective function.


By default it is set to 1e-09.


.. raw:: html

    </li>

    <li>

**ineq_tolerance** : *<class 'float'>, optional*

The tolerance on the inequality constraints.


By default it is set to 0.0001.


.. raw:: html

    </li>

    <li>

**iprint** : *<class 'int'>, optional*

The flag to control the frequency of output.

Default is no output.


By default it is set to -1.


.. raw:: html

    </li>

    <li>

**kkt_tol_abs** : *<class 'float'>, optional*

The absolute tolerance on the KKT residual norm.

If ``inf`` this criterion is not activated.


By default it is set to inf.


.. raw:: html

    </li>

    <li>

**kkt_tol_rel** : *<class 'float'>, optional*

The relative tolerance on the KKT residual norm.

If ``inf`` this criterion is not activated.


By default it is set to inf.


.. raw:: html

    </li>

    <li>

**log_problem** : *<class 'bool'>, optional*

Whether to log the definition and result of the problem.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**max_iter** : *<class 'int'>, optional*

The maximum number of iterations.


By default it is set to 1000.


.. raw:: html

    </li>

    <li>

**max_time** : *<class 'float'>, optional*

The maximum runtime in seconds, disabled if 0.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**normalize_design_space** : *<class 'bool'>, optional*

Whether to normalize the design space variables between 0 and 1.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**reset_iteration_counters** : *<class 'bool'>, optional*

Whether to reset the iteration counters before each execution.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**round_ints** : *<class 'bool'>, optional*

Whether to round the integer variables.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**scaling_threshold** : *typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional*

The threshold on the reference function value that triggers scaling.

If ``None``, do not scale the functions.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**stop_crit_n_x** : *<class 'int'>, optional*

The minimum number of design vectors to consider in the stopping criteria.


By default it is set to 3.


.. raw:: html

    </li>

    <li>

**store_jacobian** : *<class 'bool'>, optional*

Whether to store the Jacobian matrices in the database.

This argument is ignored when the ``use_database`` option is ``False``.
If a gradient-based algorithm is used,
this option cannot be set along with kkt options.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_database** : *<class 'bool'>, optional*

Whether to wrap the functions in the database.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_one_line_progress_bar** : *<class 'bool'>, optional*

Whether to log the progress bar on a single line.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**xtol_abs** : *<class 'float'>, optional*

The absolute tolerance on the design parameters.


By default it is set to 1e-09.


.. raw:: html

    </li>

    <li>

**xtol_rel** : *<class 'float'>, optional*

The relative tolerance on the design parameters.


By default it is set to 1e-09.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _Scipy_MILP_options:

Scipy_MILP
----------



Module: :class:`gemseo.algos.opt.scipy_milp.scipy_milp`


:code:`from gemseo.settings.opt import SciPyMILP_Settings`



Mixed-integer linear programming



More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/scipy.optimize.milp.html.



















































































































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**disp** : *<class 'bool'>, optional*

Whether to print optimization status during optimization.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**enable_progress_bar** : *typing.Optional[bool], optional*

Whether to enable the progress bar in the optimization log.

If ``None``, use the global value of ``enable_progress_bar`` (see the
``configure`` function to change it globally).


By default it is set to None.


.. raw:: html

    </li>

    <li>

**eq_tolerance** : *<class 'float'>, optional*

The tolerance on the equality constraints.


By default it is set to 0.01.


.. raw:: html

    </li>

    <li>

**ftol_abs** : *<class 'float'>, optional*

The absolute tolerance on the objective function.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**ftol_rel** : *<class 'float'>, optional*

The relative tolerance on the objective function.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**ineq_tolerance** : *<class 'float'>, optional*

The tolerance on the inequality constraints.


By default it is set to 0.0001.


.. raw:: html

    </li>

    <li>

**log_problem** : *<class 'bool'>, optional*

Whether to log the definition and result of the problem.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**max_iter** : *<class 'int'>, optional*

The maximum number of iterations.


By default it is set to 1000.


.. raw:: html

    </li>

    <li>

**max_time** : *<class 'float'>, optional*

The maximum runtime in seconds, disabled if 0.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**mip_rel_gap** : *<class 'float'>, optional*

The termination criterion for MIP solver.

            The solver will terminate when the gap between the primal objective value
            and the dual objective bound, scaled by the primal objective value, is <=
            mip_rel_gap.
            


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**node_limit** : *<class 'int'>, optional*

The maximum number of nodes to solve before stopping.


By default it is set to 1000.


.. raw:: html

    </li>

    <li>

**normalize_design_space** : *<class 'bool'>, optional*

Whether to normalize the design space variables between 0 and 1.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**presolve** : *<class 'bool'>, optional*

Whether to perform a preliminary analysis on the problem before solving.

            It attempts to detect infeasibility, unboundedness or problem
            simplifications.
            


By default it is set to True.


.. raw:: html

    </li>

    <li>

**reset_iteration_counters** : *<class 'bool'>, optional*

Whether to reset the iteration counters before each execution.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**round_ints** : *<class 'bool'>, optional*

Whether to round the integer variables.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**scaling_threshold** : *typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional*

The threshold on the reference function value that triggers scaling.

If ``None``, do not scale the functions.


By default it is set to None.


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    </li>

    <li>

**stop_crit_n_x** : *<class 'int'>, optional*

The minimum number of design vectors to consider in the stopping criteria.


By default it is set to 3.


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    </li>

    <li>

**store_jacobian** : *<class 'bool'>, optional*

Whether to store the Jacobian matrices in the database.

This argument is ignored when the ``use_database`` option is ``False``.
If a gradient-based algorithm is used,
this option cannot be set along with kkt options.


By default it is set to True.


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    </li>

    <li>

**use_database** : *<class 'bool'>, optional*

Whether to wrap the functions in the database.


By default it is set to True.


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    </li>

    <li>

**use_one_line_progress_bar** : *<class 'bool'>, optional*

Whether to log the progress bar on a single line.


By default it is set to False.


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    </li>

    <li>

**xtol_abs** : *<class 'float'>, optional*

The absolute tolerance on the design parameters.


By default it is set to 0.0.


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    </li>

    <li>

**xtol_rel** : *<class 'float'>, optional*

The relative tolerance on the design parameters.


By default it is set to 0.0.


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    </li>

    </ul>
    </dd>
    </dl>



.. _TNC_options:

TNC
---



Module: :class:`gemseo.algos.opt.scipy_local.scipy_local`


:code:`from gemseo.settings.opt import TNC_Settings`



Truncated Newton (TNC) algorithm implemented in SciPy library



More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/optimize.minimize-tnc.html.





























































































































































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**accuracy** : *<class 'float'>, optional*

The relative precision for finite difference calculations.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**disp** : *<class 'bool'>, optional*

Whether to print convergence messages.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**enable_progress_bar** : *typing.Optional[bool], optional*

Whether to enable the progress bar in the optimization log.

If ``None``, use the global value of ``enable_progress_bar`` (see the
``configure`` function to change it globally).


By default it is set to None.


.. raw:: html

    </li>

    <li>

**eq_tolerance** : *<class 'float'>, optional*

The tolerance on the equality constraints.


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**eta** : *<class 'float'>, optional*

The severity of the line search.


By default it is set to -1.


.. raw:: html

    </li>

    <li>

**ftol_abs** : *<class 'float'>, optional*

The absolute tolerance on the objective function.


By default it is set to 1e-09.


.. raw:: html

    </li>

    <li>

**ftol_rel** : *<class 'float'>, optional*

The relative tolerance on the objective function.


By default it is set to 1e-09.


.. raw:: html

    </li>

    <li>

**gtol** : *<class 'float'>, optional*

The precision goal for the projected gradient value to stop the algorithm.


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**ineq_tolerance** : *<class 'float'>, optional*

The tolerance on the inequality constraints.


By default it is set to 0.0001.


.. raw:: html

    </li>

    <li>

**kkt_tol_abs** : *<class 'float'>, optional*

The absolute tolerance on the KKT residual norm.

If ``inf`` this criterion is not activated.


By default it is set to inf.


.. raw:: html

    </li>

    <li>

**kkt_tol_rel** : *<class 'float'>, optional*

The relative tolerance on the KKT residual norm.

If ``inf`` this criterion is not activated.


By default it is set to inf.


.. raw:: html

    </li>

    <li>

**log_problem** : *<class 'bool'>, optional*

Whether to log the definition and result of the problem.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**max_iter** : *<class 'int'>, optional*

The maximum number of iterations.


By default it is set to 1000.


.. raw:: html

    </li>

    <li>

**max_time** : *<class 'float'>, optional*

The maximum runtime in seconds, disabled if 0.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**maxCGit** : *<class 'int'>, optional*

The maximum number of hessian-vector evaluations per main iteration.


By default it is set to -1.


.. raw:: html

    </li>

    <li>

**minfev** : *<class 'float'>, optional*

The minimum function value estimate.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**normalize_design_space** : *<class 'bool'>, optional*

Whether to normalize the design space variables between 0 and 1.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**offset** : *typing.Optional[float], optional*

The value to subtract from each variable.

If ``None``, the offsets are (up+low)/2 for interval bounded variables and
x for the others.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**rescale** : *<class 'float'>, optional*

The log10 scaling factor used to trigger the objectiv function rescaling.


By default it is set to 1.3.


.. raw:: html

    </li>

    <li>

**reset_iteration_counters** : *<class 'bool'>, optional*

Whether to reset the iteration counters before each execution.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**round_ints** : *<class 'bool'>, optional*

Whether to round the integer variables.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**scaling_threshold** : *typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional*

The threshold on the reference function value that triggers scaling.

If ``None``, do not scale the functions.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**stepmx** : *<class 'float'>, optional*

The maximum step for the line search (may be increased during call).


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**stop_crit_n_x** : *<class 'int'>, optional*

The minimum number of design vectors to consider in the stopping criteria.


By default it is set to 3.


.. raw:: html

    </li>

    <li>

**store_jacobian** : *<class 'bool'>, optional*

Whether to store the Jacobian matrices in the database.

This argument is ignored when the ``use_database`` option is ``False``.
If a gradient-based algorithm is used,
this option cannot be set along with kkt options.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_database** : *<class 'bool'>, optional*

Whether to wrap the functions in the database.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**use_one_line_progress_bar** : *<class 'bool'>, optional*

Whether to log the progress bar on a single line.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**xtol_abs** : *<class 'float'>, optional*

The absolute tolerance on the design parameters.


By default it is set to 1e-09.


.. raw:: html

    </li>

    <li>

**xtol_rel** : *<class 'float'>, optional*

The relative tolerance on the design parameters.


By default it is set to 1e-09.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>