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

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_exterior_penalty_plot_exterior_penalty_sobieski.py>`
        to download the full example code

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

.. _sphx_glr_examples_exterior_penalty_plot_exterior_penalty_sobieski.py:


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

.. GENERATED FROM PYTHON SOURCE LINES 22-54

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 54-66

.. code-block:: Python

    from __future__ import annotations

    from gemseo import configure_logger
    from gemseo import create_discipline
    from gemseo import create_scenario
    from gemseo 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.design_space import SobieskiDesignSpace

    configure_logger()





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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 67-73

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 73-81

.. code-block:: Python


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








.. GENERATED FROM PYTHON SOURCE LINES 82-89

.. tip::

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

   See :ref:`api`.

.. GENERATED FROM PYTHON SOURCE LINES 91-107

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 ``disciplines``, the names of the formulation,
the name of the objective function and the design space.

- The ``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
  :func:`.create_design_space` and
  :meth:`~gemseo.algos.design_space.DesignSpace.add_variable`. In this case,
  we will use ``SobieskiDesignSpace`` already defined in |g|.

.. GENERATED FROM PYTHON SOURCE LINES 107-109

.. code-block:: Python

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







.. GENERATED FROM PYTHON SOURCE LINES 110-142

.. 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 ``formulation`` classname (here, ``"MDF"``) shall be passed to
  the scenario to select them.
- The list of available formulations can be obtained by using
  :func:`.get_available_formulations`.

.. GENERATED FROM PYTHON SOURCE LINES 142-143

.. code-block:: Python

    get_available_formulations()




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

 .. code-block:: none


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



.. GENERATED FROM PYTHON SOURCE LINES 144-148

- :math:`y\_4` corresponds to the ``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 148-150

.. code-block:: Python

    get_all_outputs(disciplines)
    get_all_inputs(disciplines)




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

 .. code-block:: none


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



.. GENERATED FROM PYTHON SOURCE LINES 151-154

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 154-161

.. code-block:: Python

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







.. GENERATED FROM PYTHON SOURCE LINES 162-176

The range function (:math:`y\_4`) should be maximized. However, optimizers
minimize functions by default. Which is why, when creating the scenario, the argument
``maximize_objective`` shall be set to ``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 176-177

.. code-block:: Python

    scenario.set_differentiation_method()







.. GENERATED FROM PYTHON SOURCE LINES 178-203

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 204-206

.. code-block:: Python

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







.. GENERATED FROM PYTHON SOURCE LINES 207-209

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

.. GENERATED FROM PYTHON SOURCE LINES 209-212

.. code-block:: Python

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







.. GENERATED FROM PYTHON SOURCE LINES 213-215

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 215-217

.. code-block:: Python

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




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

 .. code-block:: none

        INFO - 08:57:37:  
        INFO - 08:57:37: *** Start MDOScenario execution ***
        INFO - 08:57:37: MDOScenario
        INFO - 08:57:37:    Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure
        INFO - 08:57:37:    MDO formulation: MDF
        INFO - 08:57:37: Optimization problem:
        INFO - 08:57:37:    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 - 08:57:37:    with respect to x_1, x_2, x_3, x_shared
        INFO - 08:57:37:    over the design space:
        INFO - 08:57:37:       +-------------+-------------+-------+-------------+-------+
        INFO - 08:57:37:       | Name        | Lower bound | Value | Upper bound | Type  |
        INFO - 08:57:37:       +-------------+-------------+-------+-------------+-------+
        INFO - 08:57:37:       | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
        INFO - 08:57:37:       | x_shared[1] |    30000    | 45000 |    60000    | float |
        INFO - 08:57:37:       | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
        INFO - 08:57:37:       | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
        INFO - 08:57:37:       | x_shared[4] |      40     |   55  |      70     | float |
        INFO - 08:57:37:       | x_shared[5] |     500     |  1000 |     1500    | float |
        INFO - 08:57:37:       | x_1[0]      |     0.1     |  0.25 |     0.4     | float |
        INFO - 08:57:37:       | x_1[1]      |     0.75    |   1   |     1.25    | float |
        INFO - 08:57:37:       | x_2         |     0.75    |   1   |     1.25    | float |
        INFO - 08:57:37:       | x_3         |     0.1     |  0.5  |      1      | float |
        INFO - 08:57:37:       +-------------+-------------+-------+-------------+-------+
        INFO - 08:57:37: Solving optimization problem with algorithm L-BFGS-B:
        INFO - 08:57:37:     10%|█         | 1/10 [00:00<00:01,  8.94 it/sec, obj=-53.3]
        INFO - 08:57:37:     20%|██        | 2/10 [00:00<00:01,  6.33 it/sec, obj=-401]
        INFO - 08:57:38:     30%|███       | 3/10 [00:00<00:01,  5.98 it/sec, obj=103]
        INFO - 08:57:38:     40%|████      | 4/10 [00:00<00:01,  5.65 it/sec, obj=-488]
        INFO - 08:57:38:     50%|█████     | 5/10 [00:00<00:00,  5.46 it/sec, obj=-489]
        INFO - 08:57:38:     60%|██████    | 6/10 [00:01<00:00,  5.34 it/sec, obj=-489]
        INFO - 08:57:38:     70%|███████   | 7/10 [00:01<00:00,  5.26 it/sec, obj=-489]
        INFO - 08:57:39:     80%|████████  | 8/10 [00:01<00:00,  5.20 it/sec, obj=-489]
        INFO - 08:57:39:     90%|█████████ | 9/10 [00:01<00:00,  5.15 it/sec, obj=-489]
        INFO - 08:57:39:    100%|██████████| 10/10 [00:01<00:00,  5.11 it/sec, obj=-489]
        INFO - 08:57:39: Optimization result:
        INFO - 08:57:39:    Optimizer info:
        INFO - 08:57:39:       Status: None
        INFO - 08:57:39:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
        INFO - 08:57:39:       Number of calls to the objective function by the optimizer: 12
        INFO - 08:57:39:    Solution:
        INFO - 08:57:39:       Objective: -489.2416290389368
        INFO - 08:57:39:       Design space:
        INFO - 08:57:39:          +-------------+-------------+--------------------+-------------+-------+
        INFO - 08:57:39:          | Name        | Lower bound |       Value        | Upper bound | Type  |
        INFO - 08:57:39:          +-------------+-------------+--------------------+-------------+-------+
        INFO - 08:57:39:          | x_shared[0] |     0.01    |        0.09        |     0.09    | float |
        INFO - 08:57:39:          | x_shared[1] |    30000    |       60000        |    60000    | float |
        INFO - 08:57:39:          | x_shared[2] |     1.4     |        1.4         |     1.8     | float |
        INFO - 08:57:39:          | x_shared[3] |     2.5     |        2.5         |     8.5     | float |
        INFO - 08:57:39:          | x_shared[4] |      40     |         70         |      70     | float |
        INFO - 08:57:39:          | x_shared[5] |     500     |        1500        |     1500    | float |
        INFO - 08:57:39:          | x_1[0]      |     0.1     | 0.248653494277963  |     0.4     | float |
        INFO - 08:57:39:          | x_1[1]      |     0.75    |        0.75        |     1.25    | float |
        INFO - 08:57:39:          | x_2         |     0.75    |        0.75        |     1.25    | float |
        INFO - 08:57:39:          | x_3         |     0.1     | 0.2584061783719241 |      1      | float |
        INFO - 08:57:39:          +-------------+-------------+--------------------+-------------+-------+
        INFO - 08:57:39: *** End MDOScenario execution (time: 0:00:02.095458) ***

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



.. GENERATED FROM PYTHON SOURCE LINES 218-222

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

.. GENERATED FROM PYTHON SOURCE LINES 222-225

.. code-block:: Python

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



.. image-sg:: /examples/exterior_penalty/images/sphx_glr_plot_exterior_penalty_sobieski_001.png
   :alt: History plot
   :srcset: /examples/exterior_penalty/images/sphx_glr_plot_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 0x7f8b206d4e80>



.. GENERATED FROM PYTHON SOURCE LINES 226-231

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 231-251

.. code-block:: Python

    design_space.set_current_value(x_0)
    scenario_2 = create_scenario(
        disciplines,
        "MDF",
        "y_4",
        design_space,
        maximize_objective=True,
    )
    for constraint in ["g_1", "g_2", "g_3"]:
        scenario_2.add_constraint(constraint, constraint_type="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_plot_exterior_penalty_sobieski_002.png
         :alt: History plot
         :srcset: /examples/exterior_penalty/images/sphx_glr_plot_exterior_penalty_sobieski_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/exterior_penalty/images/sphx_glr_plot_exterior_penalty_sobieski_003.png
         :alt: History plot
         :srcset: /examples/exterior_penalty/images/sphx_glr_plot_exterior_penalty_sobieski_003.png
         :class: sphx-glr-multi-img


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

 .. code-block:: none

        INFO - 08:57:39:  
        INFO - 08:57:39: *** Start MDOScenario execution ***
        INFO - 08:57:39: MDOScenario
        INFO - 08:57:39:    Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure
        INFO - 08:57:39:    MDO formulation: MDF
        INFO - 08:57:39: Optimization problem:
        INFO - 08:57:39:    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 - 08:57:39:    with respect to x_1, x_2, x_3, x_shared
        INFO - 08:57:39:    over the design space:
        INFO - 08:57:39:       +-------------+-------------+-------+-------------+-------+
        INFO - 08:57:39:       | Name        | Lower bound | Value | Upper bound | Type  |
        INFO - 08:57:39:       +-------------+-------------+-------+-------------+-------+
        INFO - 08:57:39:       | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
        INFO - 08:57:39:       | x_shared[1] |    30000    | 45000 |    60000    | float |
        INFO - 08:57:39:       | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
        INFO - 08:57:39:       | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
        INFO - 08:57:39:       | x_shared[4] |      40     |   55  |      70     | float |
        INFO - 08:57:39:       | x_shared[5] |     500     |  1000 |     1500    | float |
        INFO - 08:57:39:       | x_1[0]      |     0.1     |  0.25 |     0.4     | float |
        INFO - 08:57:39:       | x_1[1]      |     0.75    |   1   |     1.25    | float |
        INFO - 08:57:39:       | x_2         |     0.75    |   1   |     1.25    | float |
        INFO - 08:57:39:       | x_3         |     0.1     |  0.5  |      1      | float |
        INFO - 08:57:39:       +-------------+-------------+-------+-------------+-------+
        INFO - 08:57:39: Solving optimization problem with algorithm L-BFGS-B:
        INFO - 08:57:41:      1%|          | 6/1000 [00:01<03:00,  5.50 it/sec, obj=-0.428]
        INFO - 08:57:41:      1%|          | 7/1000 [00:01<03:00,  5.51 it/sec, obj=-0.504]
        INFO - 08:57:41:      1%|          | 8/1000 [00:01<02:59,  5.54 it/sec, obj=-0.413]
        INFO - 08:57:41:      1%|          | 9/1000 [00:01<02:58,  5.56 it/sec, obj=-0.521]
        INFO - 08:57:41:      1%|          | 10/1000 [00:01<02:57,  5.58 it/sec, obj=-0.537]
        INFO - 08:57:41:      1%|          | 11/1000 [00:01<02:56,  5.60 it/sec, obj=-0.54]
        INFO - 08:57:42:      1%|          | 12/1000 [00:02<02:56,  5.60 it/sec, obj=-0.541]
        INFO - 08:57:42:      1%|▏         | 13/1000 [00:02<02:56,  5.60 it/sec, obj=-0.521]
        INFO - 08:57:42:      1%|▏         | 14/1000 [00:02<02:55,  5.61 it/sec, obj=-0.541]
        INFO - 08:57:42:      2%|▏         | 15/1000 [00:02<02:55,  5.61 it/sec, obj=4.92]
        INFO - 08:57:42:      2%|▏         | 16/1000 [00:02<02:55,  5.62 it/sec, obj=-0.542]
        INFO - 08:57:42:      2%|▏         | 17/1000 [00:03<02:54,  5.64 it/sec, obj=-0.542]
        INFO - 08:57:43:      2%|▏         | 18/1000 [00:03<02:53,  5.65 it/sec, obj=0.751]
        INFO - 08:57:43:      2%|▏         | 19/1000 [00:03<02:53,  5.66 it/sec, obj=-0.542]
        INFO - 08:57:43:      2%|▏         | 20/1000 [00:03<02:53,  5.66 it/sec, obj=-0.589]
        INFO - 08:57:43:      2%|▏         | 21/1000 [00:03<02:53,  5.65 it/sec, obj=28.5]
        INFO - 08:57:43:      2%|▏         | 22/1000 [00:03<02:53,  5.64 it/sec, obj=-0.601]
        INFO - 08:57:44:      2%|▏         | 23/1000 [00:04<02:53,  5.63 it/sec, obj=-0.609]
        INFO - 08:57:44:      2%|▏         | 24/1000 [00:04<02:53,  5.63 it/sec, obj=2.4]
        INFO - 08:57:44:      2%|▎         | 25/1000 [00:04<02:53,  5.62 it/sec, obj=-0.625]
        INFO - 08:57:44:      3%|▎         | 26/1000 [00:04<02:53,  5.61 it/sec, obj=-0.639]
        INFO - 08:57:44:      3%|▎         | 27/1000 [00:04<02:53,  5.61 it/sec, obj=-0.311]
        INFO - 08:57:44:      3%|▎         | 28/1000 [00:04<02:53,  5.60 it/sec, obj=-0.645]
        INFO - 08:57:45:      3%|▎         | 29/1000 [00:05<02:53,  5.60 it/sec, obj=-0.65]
        INFO - 08:57:45:      3%|▎         | 30/1000 [00:05<02:53,  5.59 it/sec, obj=-0.611]
        INFO - 08:57:45:      3%|▎         | 31/1000 [00:05<02:53,  5.58 it/sec, obj=2.98]
        INFO - 08:57:45:      3%|▎         | 32/1000 [00:05<02:53,  5.57 it/sec, obj=-0.651]
        INFO - 08:57:45:      3%|▎         | 33/1000 [00:05<02:53,  5.57 it/sec, obj=0.77]
        INFO - 08:57:46:      3%|▎         | 34/1000 [00:06<02:53,  5.56 it/sec, obj=-0.652]
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        INFO - 08:58:05:     13%|█▎        | 126/1000 [00:25<02:55,  4.98 it/sec, obj=-3.98]
        INFO - 08:58:05:     13%|█▎        | 127/1000 [00:25<02:55,  4.98 it/sec, obj=-3.98]
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        INFO - 08:58:06:     13%|█▎        | 130/1000 [00:26<02:54,  4.98 it/sec, obj=-3.98]
        INFO - 08:58:06:     13%|█▎        | 131/1000 [00:26<02:54,  4.97 it/sec, obj=-3.98]
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        INFO - 08:58:06:     13%|█▎        | 134/1000 [00:26<02:54,  4.97 it/sec, obj=-3.98]
        INFO - 08:58:07: Optimization result:
        INFO - 08:58:07:    Optimizer info:
        INFO - 08:58:07:       Status: 0
        INFO - 08:58:07:       Message: CONVERGENCE: NORM_OF_PROJECTED_GRADIENT_<=_PGTOL
        INFO - 08:58:07:       Number of calls to the objective function by the optimizer: 136
        INFO - 08:58:07:    Solution:
        INFO - 08:58:07:       Objective: -3.9803860964876963
        INFO - 08:58:07:       Design space:
        INFO - 08:58:07:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 08:58:07:          | Name        | Lower bound |        Value        | Upper bound | Type  |
        INFO - 08:58:07:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 08:58:07:          | x_shared[0] |     0.01    | 0.06101561365627294 |     0.09    | float |
        INFO - 08:58:07:          | x_shared[1] |    30000    |        60000        |    60000    | float |
        INFO - 08:58:07:          | x_shared[2] |     1.4     |         1.4         |     1.8     | float |
        INFO - 08:58:07:          | x_shared[3] |     2.5     |         2.5         |     8.5     | float |
        INFO - 08:58:07:          | x_shared[4] |      40     |          70         |      70     | float |
        INFO - 08:58:07:          | x_shared[5] |     500     |         1500        |     1500    | float |
        INFO - 08:58:07:          | x_1[0]      |     0.1     |         0.4         |     0.4     | float |
        INFO - 08:58:07:          | x_1[1]      |     0.75    |         0.75        |     1.25    | float |
        INFO - 08:58:07:          | x_2         |     0.75    |         0.75        |     1.25    | float |
        INFO - 08:58:07:          | x_3         |     0.1     |  0.1562913023426308 |      1      | float |
        INFO - 08:58:07:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 08:58:07: *** End MDOScenario execution (time: 0:00:27.093792) ***

    <gemseo.post.basic_history.BasicHistory object at 0x7f8b0b09cbe0>



.. GENERATED FROM PYTHON SOURCE LINES 252-254

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 30.119 seconds)


.. _sphx_glr_download_examples_exterior_penalty_plot_exterior_penalty_sobieski.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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