.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/exterior_penalty/exterior_penalty_sobieski.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        Click :ref:`here <sphx_glr_download_examples_exterior_penalty_exterior_penalty_sobieski.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_exterior_penalty_exterior_penalty_sobieski.py:


Example for exterior penalty applied to the Sobieski test case.
===============================================================

.. GENERATED FROM PYTHON SOURCE LINES 21-53

This section describes how to set up and solve the MDO problem relative to the
:ref:`Sobieski test case <sobieski_problem>` with |g| applying external penalty.

.. seealso::

   To start with a simpler MDO problem, and for a detailed description
   of how to plug a test case into |g|, see :ref:`sellar_mdo`.


.. _sobieski_use_case:

Solving with an :ref:`MDF formulation <mdf_formulation>`
--------------------------------------------------------

In this example, we solve the range optimization using the following
:ref:`MDF formulation <mdf_formulation>`:

- The :ref:`MDF formulation <mdf_formulation>` couples all the disciplines
  during the :ref:`mda` at each optimization iteration.
- All the :term:`design variables` are equally treated, concatenated in a
  single vector and given to a single :term:`optimization algorithm` as the
  unknowns of the problem.
- There is no specific :term:`constraint` due to the :ref:`MDF formulation
  <mdf_formulation>`.
- Only the design :term:`constraints` :math:`g\_1`, :math:`g\_2` and
  :math:`g\_3` are added to the problem.
- The :term:`objective function` is the range (the :math:`y\_4` variable in
  the model), computed after the :ref:`mda`.

Imports
-------
All the imports needed for the tutorials are performed here.

.. GENERATED FROM PYTHON SOURCE LINES 53-65

.. code-block:: default

    from __future__ import annotations

    from gemseo.api import configure_logger
    from gemseo.api import create_discipline
    from gemseo.api import create_scenario
    from gemseo.api import get_available_formulations
    from gemseo.disciplines.utils import get_all_inputs
    from gemseo.disciplines.utils import get_all_outputs
    from gemseo.problems.sobieski.core.problem import SobieskiProblem

    configure_logger()





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 66-72

Step 1: Creation of :class:`.MDODiscipline`
-------------------------------------------

To build the scenario, we first instantiate the disciplines. Here, the
disciplines themselves have already been
developed and interfaced with |g| (see :ref:`benchmark_problems`).

.. GENERATED FROM PYTHON SOURCE LINES 72-82

.. code-block:: default


    disciplines = create_discipline(
        [
            "SobieskiPropulsion",
            "SobieskiAerodynamics",
            "SobieskiMission",
            "SobieskiStructure",
        ]
    )








.. GENERATED FROM PYTHON SOURCE LINES 83-90

.. tip::

   For the disciplines that are not interfaced with |g|, the |g|'s
   :mod:`~gemseo.api` eases the creation of disciplines without having
   to import them.

   See :ref:`api`.

.. GENERATED FROM PYTHON SOURCE LINES 92-108

Step 2: Creation of :class:`.Scenario`
--------------------------------------

The scenario delegates the creation of the optimization problem to the
:ref:`MDO formulation <mdo_formulations>`.

Therefore, it needs the list of :code:`disciplines`, the names of the formulation,
the name of the objective function and the design space.

- The :code:`design_space` (shown below for reference)
  defines the unknowns of the optimization problem, and their bounds. It contains
  all the design variables needed by the :ref:`MDF formulation <mdf_formulation>`.
  It can be imported from a text file, or created from scratch with the methods
  :meth:`~gemseo.api.create_design_space` and
  :meth:`~gemseo.algos.design_space.DesignSpace.add_variable`. In this case,
  we will retrieve it from the ``SobieskiProblem`` already defined in |g|.

.. GENERATED FROM PYTHON SOURCE LINES 108-110

.. code-block:: default

    design_space = SobieskiProblem().design_space
    x_0 = design_space.get_current_value(as_dict=True)







.. GENERATED FROM PYTHON SOURCE LINES 111-143

.. code::


          name      lower_bound      value      upper_bound  type
          x_shared      0.01          0.05          0.09     float
          x_shared    30000.0       45000.0       60000.0    float
          x_shared      1.4           1.6           1.8      float
          x_shared      2.5           5.5           8.5      float
          x_shared      40.0          55.0          70.0     float
          x_shared     500.0         1000.0        1500.0    float
          x_1           0.1           0.25          0.4      float
          x_1           0.75          1.0           1.25     float
          x_2           0.75          1.0           1.25     float
          x_3           0.1           0.5           1.0      float
          y_14        24850.0    50606.9741711    77100.0    float
          y_14        -7700.0    7306.20262124    45000.0    float
          y_32         0.235       0.50279625      0.795     float
          y_31         2960.0    6354.32430691    10185.0    float
          y_24          0.44       4.15006276      11.13     float
          y_34          0.44       1.10754577       1.98     float
          y_23         3365.0    12194.2671934    26400.0    float
          y_21        24850.0    50606.9741711    77250.0    float
          y_12        24850.0      50606.9742     77250.0    float
          y_12          0.45          0.95          1.5      float

- The available :ref:`MDO formulations <mdo_formulations>` are located in the
  **gemseo.formulations** package, see :ref:`extending-gemseo` for extending
  GEMSEO with other formulations.
- The :code:`formulation` classname (here, :code:`"MDF"`) shall be passed to
  the scenario to select them.
- The list of available formulations can be obtained by using
  :meth:`~gemseo.api.get_available_formulations`.

.. GENERATED FROM PYTHON SOURCE LINES 143-144

.. code-block:: default

    get_available_formulations()




.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    ['BiLevel', 'DisciplinaryOpt', 'IDF', 'MDF']



.. GENERATED FROM PYTHON SOURCE LINES 145-149

- :math:`y\_4` corresponds to the :code:`objective_name`. This name must be one
  of the disciplines outputs, here the ``SobieskiMission`` discipline. The list of
  all outputs of the disciplines can be obtained by using
  :meth:`~gemseo.disciplines.utils.get_all_outputs`:

.. GENERATED FROM PYTHON SOURCE LINES 149-151

.. code-block:: default

    get_all_outputs(disciplines)
    get_all_inputs(disciplines)




.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    ['y_23', 'x_3', 'c_3', 'y_14', 'y_34', 'c_1', 'c_2', 'c_0', 'y_31', 'y_24', 'c_4', 'x_2', 'y_12', 'x_shared', 'y_21', 'x_1', 'y_32']



.. GENERATED FROM PYTHON SOURCE LINES 152-155

From these :class:`~gemseo.core.discipline.MDODiscipline`, design space,
:ref:`MDO formulation <mdo_formulations>` name and objective function name,
we build the scenario:

.. GENERATED FROM PYTHON SOURCE LINES 155-162

.. code-block:: default

    scenario = create_scenario(
        disciplines,
        formulation="MDF",
        maximize_objective=True,
        objective_name="y_4",
        design_space=design_space,
    )







.. GENERATED FROM PYTHON SOURCE LINES 163-177

The range function (:math:`y\_4`) should be maximized. However, optimizers
minimize functions by default. Which is why, when creating the scenario, the argument
:code:`maximize_objective` shall be set to :code:`True`.

Differentiation method
~~~~~~~~~~~~~~~~~~~~~~

We may choose the way derivatives are computed:


**Function derivatives.** As analytical disciplinary derivatives are
available for the Sobieski test-case, they can be used instead of computing
the derivatives with finite-differences or with the complex-step method.
The easiest way to set a method is to let the optimizer determine it:

.. GENERATED FROM PYTHON SOURCE LINES 177-178

.. code-block:: default

    scenario.set_differentiation_method()







.. GENERATED FROM PYTHON SOURCE LINES 179-204

The default behavior of the optimizer triggers :term:`finite differences`.
It corresponds to:

.. code::

  scenario.set_differentiation_method("finite_differences",1e-7)

It it also possible to differentiate functions by means of the
:term:`complex step` method:

.. code::

  scenario.set_differentiation_method("complex_step",1e-30j)

Constraints
~~~~~~~~~~~

Similarly to the objective function, the constraints names are a subset
of the disciplines' outputs. They can be obtained by using
:meth:`~gemseo.disciplines.utils.get_all_outputs`.

The formulation has a powerful feature to automatically dispatch the constraints
(:math:`g\_1, g\_2, g\_3`) and plug them to the optimizers depending on
the formulation. To do that, we use the method
:meth:`~gemseo.core.scenario.Scenario.add_constraint`:

.. GENERATED FROM PYTHON SOURCE LINES 205-207

.. code-block:: default

    for constraint in ["g_1", "g_2", "g_3"]:
        scenario.add_constraint(constraint, "ineq")







.. GENERATED FROM PYTHON SOURCE LINES 208-210

Step 3: Apply the exterior penalty and execute the scenario
-----------------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 210-213

.. code-block:: default

    scenario.formulation.opt_problem.apply_exterior_penalty(
        objective_scale=10.0, scale_inequality=10.0
    )







.. GENERATED FROM PYTHON SOURCE LINES 214-216

In this way the L-BFGS-B algorithm can be used to solve the optimization problem.
Note that this algorithm is not suited for constrained optimization problems.

.. GENERATED FROM PYTHON SOURCE LINES 216-218

.. code-block:: default

    algo_args = {"max_iter": 10, "algo": "L-BFGS-B"}
    scenario.execute(algo_args)




.. rst-class:: sphx-glr-script-out

 .. code-block:: none

        INFO - 16:59:55:  
        INFO - 16:59:55: *** Start MDOScenario execution ***
        INFO - 16:59:55: MDOScenario
        INFO - 16:59:55:    Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure
        INFO - 16:59:55:    MDO formulation: MDF
        INFO - 16:59:55: Optimization problem:
        INFO - 16:59:55:    minimize -y_4/10.0+pos_sum_g_1+pos_sum_g_2+pos_sum_g_3(x_1, x_2, x_3, x_shared) = -y_4(x_shared, x_1, x_2, x_3)/10.0+sum(heaviside()***2)+sum(heaviside()***2)+sum(heaviside()***2)
        INFO - 16:59:55:    with respect to x_1, x_2, x_3, x_shared
        INFO - 16:59:55:    over the design space:
        INFO - 16:59:55:    +-------------+-------------+-------+-------------+-------+
        INFO - 16:59:55:    | name        | lower_bound | value | upper_bound | type  |
        INFO - 16:59:55:    +-------------+-------------+-------+-------------+-------+
        INFO - 16:59:55:    | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
        INFO - 16:59:55:    | x_shared[1] |    30000    | 45000 |    60000    | float |
        INFO - 16:59:55:    | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
        INFO - 16:59:55:    | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
        INFO - 16:59:55:    | x_shared[4] |      40     |   55  |      70     | float |
        INFO - 16:59:55:    | x_shared[5] |     500     |  1000 |     1500    | float |
        INFO - 16:59:55:    | x_1[0]      |     0.1     |  0.25 |     0.4     | float |
        INFO - 16:59:55:    | x_1[1]      |     0.75    |   1   |     1.25    | float |
        INFO - 16:59:55:    | x_2         |     0.75    |   1   |     1.25    | float |
        INFO - 16:59:55:    | x_3         |     0.1     |  0.5  |      1      | float |
        INFO - 16:59:55:    +-------------+-------------+-------+-------------+-------+
        INFO - 16:59:55: Solving optimization problem with algorithm L-BFGS-B:
        INFO - 16:59:55: ...   0%|          | 0/10 [00:00<?, ?it]
        INFO - 16:59:55: ...  10%|█         | 1/10 [00:00<00:00, 10.66 it/sec, obj=-53.3]
        INFO - 16:59:56: ...  20%|██        | 2/10 [00:00<00:00,  8.10 it/sec, obj=-401]
        INFO - 16:59:56: ...  30%|███       | 3/10 [00:00<00:00,  7.99 it/sec, obj=103]
        INFO - 16:59:56: ...  40%|████      | 4/10 [00:00<00:00,  7.86 it/sec, obj=-488]
        INFO - 16:59:56: ...  50%|█████     | 5/10 [00:00<00:00,  7.68 it/sec, obj=-489]
        INFO - 16:59:56: ...  60%|██████    | 6/10 [00:00<00:00,  7.57 it/sec, obj=-489]
        INFO - 16:59:56: ...  70%|███████   | 7/10 [00:00<00:00,  7.49 it/sec, obj=-489]
        INFO - 16:59:56: ...  80%|████████  | 8/10 [00:01<00:00,  7.44 it/sec, obj=-489]
        INFO - 16:59:57: ...  90%|█████████ | 9/10 [00:01<00:00,  7.39 it/sec, obj=-489]
        INFO - 16:59:57: ... 100%|██████████| 10/10 [00:01<00:00,  7.36 it/sec, obj=-489]
        INFO - 16:59:57: Optimization result:
        INFO - 16:59:57:    Optimizer info:
        INFO - 16:59:57:       Status: None
        INFO - 16:59:57:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
        INFO - 16:59:57:       Number of calls to the objective function by the optimizer: 12
        INFO - 16:59:57:    Solution:
        INFO - 16:59:57:       Objective: -489.2416290390015
        INFO - 16:59:57:       Design space: 
        INFO - 16:59:57:       +-------------+-------------+--------------------+-------------+-------+
        INFO - 16:59:57:       | name        | lower_bound |       value        | upper_bound | type  |
        INFO - 16:59:57:       +-------------+-------------+--------------------+-------------+-------+
        INFO - 16:59:57:       | x_shared[0] |     0.01    |        0.09        |     0.09    | float |
        INFO - 16:59:57:       | x_shared[1] |    30000    |       60000        |    60000    | float |
        INFO - 16:59:57:       | x_shared[2] |     1.4     |        1.4         |     1.8     | float |
        INFO - 16:59:57:       | x_shared[3] |     2.5     |        2.5         |     8.5     | float |
        INFO - 16:59:57:       | x_shared[4] |      40     |         70         |      70     | float |
        INFO - 16:59:57:       | x_shared[5] |     500     |        1500        |     1500    | float |
        INFO - 16:59:57:       | x_1[0]      |     0.1     | 0.2486534942788055 |     0.4     | float |
        INFO - 16:59:57:       | x_1[1]      |     0.75    |        0.75        |     1.25    | float |
        INFO - 16:59:57:       | x_2         |     0.75    |        0.75        |     1.25    | float |
        INFO - 16:59:57:       | x_3         |     0.1     | 0.258406178372979  |      1      | float |
        INFO - 16:59:57:       +-------------+-------------+--------------------+-------------+-------+
        INFO - 16:59:57: *** End MDOScenario execution (time: 0:00:01.451289) ***

    {'max_iter': 10, 'algo': 'L-BFGS-B'}



.. GENERATED FROM PYTHON SOURCE LINES 219-223

Post-processing options
~~~~~~~~~~~~~~~~~~~~~~~
To visualize the optimization history of the constraint violation one can use the
:class:`.BasicHistory`:

.. GENERATED FROM PYTHON SOURCE LINES 223-226

.. code-block:: default

    scenario.post_process(
        "BasicHistory", variable_names=["g_1", "g_2", "g_3"], save=False, show=True
    )



.. image-sg:: /examples/exterior_penalty/images/sphx_glr_exterior_penalty_sobieski_001.png
   :alt: History plot
   :srcset: /examples/exterior_penalty/images/sphx_glr_exterior_penalty_sobieski_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    <gemseo.post.basic_history.BasicHistory object at 0x7fbc55caa490>



.. GENERATED FROM PYTHON SOURCE LINES 227-232

This solution is almost feasible.
The solution can better approximate the original problem solution increasing the value
 of `objective_scale` and  `scale_inequality` parameters.
Step 4: Rerun the scenario with increased penalty and objective scaling.
------------------------------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 232-252

.. code-block:: default

    design_space.set_current_value(x_0)
    scenario_2 = create_scenario(
        disciplines,
        formulation="MDF",
        maximize_objective=True,
        objective_name="y_4",
        design_space=design_space,
    )
    for constraint in ["g_1", "g_2", "g_3"]:
        scenario_2.add_constraint(constraint, "ineq")
    scenario_2.set_differentiation_method()
    scenario_2.formulation.opt_problem.apply_exterior_penalty(
        objective_scale=1000.0, scale_inequality=1000.0
    )
    algo_args_2 = {"max_iter": 1000, "algo": "L-BFGS-B"}
    scenario_2.execute(algo_args_2)
    scenario_2.post_process("BasicHistory", variable_names=["-y_4"], save=False, show=True)
    scenario_2.post_process(
        "BasicHistory", variable_names=["g_1", "g_2", "g_3"], save=False, show=True
    )



.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /examples/exterior_penalty/images/sphx_glr_exterior_penalty_sobieski_002.png
         :alt: History plot
         :srcset: /examples/exterior_penalty/images/sphx_glr_exterior_penalty_sobieski_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/exterior_penalty/images/sphx_glr_exterior_penalty_sobieski_003.png
         :alt: History plot
         :srcset: /examples/exterior_penalty/images/sphx_glr_exterior_penalty_sobieski_003.png
         :class: sphx-glr-multi-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

        INFO - 16:59:57:  
        INFO - 16:59:57: *** Start MDOScenario execution ***
        INFO - 16:59:57: MDOScenario
        INFO - 16:59:57:    Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure
        INFO - 16:59:57:    MDO formulation: MDF
        INFO - 16:59:57: Optimization problem:
        INFO - 16:59:57:    minimize -y_4/1000.0+pos_sum_g_1+pos_sum_g_2+pos_sum_g_3(x_1, x_2, x_3, x_shared) = -y_4(x_shared, x_1, x_2, x_3)/1000.0+sum(heaviside()***2)+sum(heaviside()***2)+sum(heaviside()***2)
        INFO - 16:59:57:    with respect to x_1, x_2, x_3, x_shared
        INFO - 16:59:57:    over the design space:
        INFO - 16:59:57:    +-------------+-------------+-------+-------------+-------+
        INFO - 16:59:57:    | name        | lower_bound | value | upper_bound | type  |
        INFO - 16:59:57:    +-------------+-------------+-------+-------------+-------+
        INFO - 16:59:57:    | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
        INFO - 16:59:57:    | x_shared[1] |    30000    | 45000 |    60000    | float |
        INFO - 16:59:57:    | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
        INFO - 16:59:57:    | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
        INFO - 16:59:57:    | x_shared[4] |      40     |   55  |      70     | float |
        INFO - 16:59:57:    | x_shared[5] |     500     |  1000 |     1500    | float |
        INFO - 16:59:57:    | x_1[0]      |     0.1     |  0.25 |     0.4     | float |
        INFO - 16:59:57:    | x_1[1]      |     0.75    |   1   |     1.25    | float |
        INFO - 16:59:57:    | x_2         |     0.75    |   1   |     1.25    | float |
        INFO - 16:59:57:    | x_3         |     0.1     |  0.5  |      1      | float |
        INFO - 16:59:57:    +-------------+-------------+-------+-------------+-------+
        INFO - 16:59:57: Solving optimization problem with algorithm L-BFGS-B:
        INFO - 16:59:57: ...   0%|          | 0/1000 [00:00<?, ?it]
        INFO - 16:59:57: ...   0%|          | 1/1000 [00:00<01:17, 12.96 it/sec, obj=27]
        INFO - 16:59:57: ...   0%|          | 2/1000 [00:00<01:51,  8.97 it/sec, obj=1.03e+4]
        INFO - 16:59:57: ...   0%|          | 3/1000 [00:00<02:00,  8.30 it/sec, obj=-.304]
        INFO - 16:59:57: ...   0%|          | 4/1000 [00:00<02:05,  7.95 it/sec, obj=-.308]
        INFO - 16:59:58: ...   0%|          | 5/1000 [00:00<02:09,  7.69 it/sec, obj=-.34]
        INFO - 16:59:58: ...   1%|          | 6/1000 [00:00<02:11,  7.58 it/sec, obj=-.428]
        INFO - 16:59:58: ...   1%|          | 7/1000 [00:00<02:09,  7.64 it/sec, obj=-.504]
        INFO - 16:59:58: ...   1%|          | 8/1000 [00:01<02:08,  7.75 it/sec, obj=-.413]
        INFO - 16:59:58: ...   1%|          | 9/1000 [00:01<02:06,  7.82 it/sec, obj=-.521]
        INFO - 16:59:58: ...   1%|          | 10/1000 [00:01<02:05,  7.90 it/sec, obj=-.537]
        INFO - 16:59:58: ...   1%|          | 11/1000 [00:01<02:04,  7.96 it/sec, obj=-.54]
        INFO - 16:59:58: ...   1%|          | 12/1000 [00:01<02:03,  8.01 it/sec, obj=-.541]
        INFO - 16:59:59: ...   1%|▏         | 13/1000 [00:01<02:02,  8.05 it/sec, obj=-.521]
        INFO - 16:59:59: ...   1%|▏         | 14/1000 [00:01<02:01,  8.10 it/sec, obj=-.541]
        INFO - 16:59:59: ...   2%|▏         | 15/1000 [00:01<02:01,  8.11 it/sec, obj=4.92]
        INFO - 16:59:59: ...   2%|▏         | 16/1000 [00:01<02:00,  8.14 it/sec, obj=-.542]
        INFO - 16:59:59: ...   2%|▏         | 17/1000 [00:02<02:00,  8.16 it/sec, obj=-.542]
        INFO - 16:59:59: ...   2%|▏         | 18/1000 [00:02<02:00,  8.18 it/sec, obj=0.751]
        INFO - 16:59:59: ...   2%|▏         | 19/1000 [00:02<01:59,  8.20 it/sec, obj=-.542]
        INFO - 16:59:59: ...   2%|▏         | 20/1000 [00:02<01:59,  8.22 it/sec, obj=-.589]
        INFO - 17:00:00: ...   2%|▏         | 21/1000 [00:02<01:59,  8.22 it/sec, obj=28.5]
        INFO - 17:00:00: ...   2%|▏         | 22/1000 [00:02<01:58,  8.22 it/sec, obj=-.601]
        INFO - 17:00:00: ...   2%|▏         | 23/1000 [00:02<01:58,  8.22 it/sec, obj=-.609]
        INFO - 17:00:00: ...   2%|▏         | 24/1000 [00:02<01:58,  8.22 it/sec, obj=2.4]
        INFO - 17:00:00: ...   2%|▎         | 25/1000 [00:03<01:58,  8.23 it/sec, obj=-.625]
        INFO - 17:00:00: ...   3%|▎         | 26/1000 [00:03<01:58,  8.23 it/sec, obj=-.639]
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        INFO - 17:00:11: Optimization result:
        INFO - 17:00:11:    Optimizer info:
        INFO - 17:00:11:       Status: None
        INFO - 17:00:11:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
        INFO - 17:00:11:       Number of calls to the objective function by the optimizer: 105
        INFO - 17:00:11:    Solution:
        INFO - 17:00:11:       Objective: -4.409273981292273
        INFO - 17:00:11:       Design space: 
        INFO - 17:00:11:       +-------------+-------------+--------------------+-------------+-------+
        INFO - 17:00:11:       | name        | lower_bound |       value        | upper_bound | type  |
        INFO - 17:00:11:       +-------------+-------------+--------------------+-------------+-------+
        INFO - 17:00:11:       | x_shared[0] |     0.01    |        0.09        |     0.09    | float |
        INFO - 17:00:11:       | x_shared[1] |    30000    |       60000        |    60000    | float |
        INFO - 17:00:11:       | x_shared[2] |     1.4     |        1.4         |     1.8     | float |
        INFO - 17:00:11:       | x_shared[3] |     2.5     |        2.5         |     8.5     | float |
        INFO - 17:00:11:       | x_shared[4] |      40     |         70         |      70     | float |
        INFO - 17:00:11:       | x_shared[5] |     500     |        1500        |     1500    | float |
        INFO - 17:00:11:       | x_1[0]      |     0.1     | 0.2601353730963641 |     0.4     | float |
        INFO - 17:00:11:       | x_1[1]      |     0.75    |        0.75        |     1.25    | float |
        INFO - 17:00:11:       | x_2         |     0.75    |        0.75        |     1.25    | float |
        INFO - 17:00:11:       | x_3         |     0.1     | 0.1563540424106258 |      1      | float |
        INFO - 17:00:11:       +-------------+-------------+--------------------+-------------+-------+
        INFO - 17:00:11: *** End MDOScenario execution (time: 0:00:13.872130) ***

    <gemseo.post.basic_history.BasicHistory object at 0x7fbc399409a0>



.. GENERATED FROM PYTHON SOURCE LINES 253-255

The solution feasibility was improved but this comes with a much higher number of
iterations.


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  15.903 seconds)


.. _sphx_glr_download_examples_exterior_penalty_exterior_penalty_sobieski.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example


    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: exterior_penalty_sobieski.py <exterior_penalty_sobieski.py>`

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: exterior_penalty_sobieski.ipynb <exterior_penalty_sobieski.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_