.. only:: html

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

        Click :ref:`here <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
=============================

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



.. code-block:: default

    from __future__ import print_function
    import openturns as ot
    import openturns.viewer as viewer
    from matplotlib import pylab as plt
    import math as m
    ot.Log.Show(ot.Log.NONE)








define the objective function


.. code-block:: default

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








define the constraints


.. code-block:: default

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








define the problem bounds


.. code-block:: default

    dim = objective.getInputDimension()
    bounds = ot.Interval([-3.] * dim, [5.] * dim)








define the problem


.. code-block:: default

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








solve the problem


.. code-block:: default

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








retrieve results


.. code-block:: default

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





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

 Out:

 .. code-block:: none

    x^= [5,-3,5,-3]




draw optimal value history


.. code-block:: default

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




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






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

   **Total running time of the script:** ( 0 minutes  0.076 seconds)


.. _sphx_glr_download_auto_numerical_methods_optimization_plot_optimization_constraints.py:


.. only :: html

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



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

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



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

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


.. only:: html

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

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