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

.. only:: html

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

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

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

.. _sphx_glr_auto_numerical_methods_optimization_plot_optimization_constraints.py:


Optimization with constraints
=============================

.. GENERATED FROM PYTHON SOURCE LINES 6-13

In this example we are going to expose methods to solve a generic optimization problem in the form

.. math::
    \min_{x\in B} f(x) \\
       g(x) = 0 \\
       h(x) \ge 0


.. GENERATED FROM PYTHON SOURCE LINES 15-21

.. code-block:: Python

    import openturns as ot
    import openturns.viewer as viewer
    from matplotlib import pylab as plt

    ot.Log.Show(ot.Log.NONE)








.. GENERATED FROM PYTHON SOURCE LINES 22-23

define the objective function

.. GENERATED FROM PYTHON SOURCE LINES 23-27

.. code-block:: Python

    objective = ot.SymbolicFunction(
        ["x1", "x2", "x3", "x4"], ["x1 + 2 * x2 - 3 * x3 + 4 * x4"]
    )








.. GENERATED FROM PYTHON SOURCE LINES 28-29

define the constraints

.. GENERATED FROM PYTHON SOURCE LINES 29-31

.. code-block:: Python

    inequality_constraint = ot.SymbolicFunction(["x1", "x2", "x3", "x4"], ["x1-x3"])








.. GENERATED FROM PYTHON SOURCE LINES 32-33

define the problem bounds

.. GENERATED FROM PYTHON SOURCE LINES 33-36

.. code-block:: Python

    dim = objective.getInputDimension()
    bounds = ot.Interval([-3.0] * dim, [5.0] * dim)








.. GENERATED FROM PYTHON SOURCE LINES 37-38

define the problem

.. GENERATED FROM PYTHON SOURCE LINES 38-43

.. code-block:: Python

    problem = ot.OptimizationProblem(objective)
    problem.setMinimization(True)
    problem.setInequalityConstraint(inequality_constraint)
    problem.setBounds(bounds)








.. GENERATED FROM PYTHON SOURCE LINES 44-45

solve the problem

.. GENERATED FROM PYTHON SOURCE LINES 45-51

.. code-block:: Python

    algo = ot.Cobyla()
    algo.setProblem(problem)
    startingPoint = [0.0] * dim
    algo.setStartingPoint(startingPoint)
    algo.run()








.. GENERATED FROM PYTHON SOURCE LINES 52-53

retrieve results

.. GENERATED FROM PYTHON SOURCE LINES 53-56

.. code-block:: Python

    result = algo.getResult()
    print("x^=", result.getOptimalPoint())





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

 .. code-block:: none

    x^= [4.90274,-3,4.90274,-3]




.. GENERATED FROM PYTHON SOURCE LINES 57-58

draw optimal value history

.. GENERATED FROM PYTHON SOURCE LINES 58-61

.. code-block:: Python

    graph = result.drawOptimalValueHistory()
    view = viewer.View(graph)
    plt.show()



.. image-sg:: /auto_numerical_methods/optimization/images/sphx_glr_plot_optimization_constraints_001.png
   :alt: Optimal value history
   :srcset: /auto_numerical_methods/optimization/images/sphx_glr_plot_optimization_constraints_001.png
   :class: sphx-glr-single-img






.. _sphx_glr_download_auto_numerical_methods_optimization_plot_optimization_constraints.py:

.. only:: html

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

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

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

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

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