.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_numerical_methods/optimization/plot_minmax_optimization.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_minmax_optimization.py>`
        to download the full example code

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

.. _sphx_glr_auto_numerical_methods_optimization_plot_minmax_optimization.py:


Mix/max search using optimization
=================================

.. GENERATED FROM PYTHON SOURCE LINES 6-7

In this example we are going to evaluate the min and max values of the output variable of interest in a domain using an optimization algorithm.

.. GENERATED FROM PYTHON SOURCE LINES 10-14

.. code-block:: Python

    import openturns as ot

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








.. GENERATED FROM PYTHON SOURCE LINES 15-16

Create the marginal distributions of the parameters

.. GENERATED FROM PYTHON SOURCE LINES 16-23

.. code-block:: Python

    dist_E = ot.Beta(0.93, 2.27, 2.8e7, 4.8e7)
    dist_F = ot.LogNormalMuSigma(30000, 9000, 15000).getDistribution()
    dist_L = ot.Uniform(250, 260)
    dist_I = ot.Beta(2.5, 1.5, 3.1e2, 4.5e2)
    marginals = [dist_E, dist_F, dist_L, dist_I]
    distribution = ot.ComposedDistribution(marginals)








.. GENERATED FROM PYTHON SOURCE LINES 24-25

Define bounds

.. GENERATED FROM PYTHON SOURCE LINES 25-29

.. code-block:: Python

    lowerBound = [marginal.computeQuantile(0.1)[0] for marginal in marginals]
    upperBound = [marginal.computeQuantile(0.9)[0] for marginal in marginals]
    bounds = ot.Interval(lowerBound, upperBound)








.. GENERATED FROM PYTHON SOURCE LINES 30-31

Create the model

.. GENERATED FROM PYTHON SOURCE LINES 31-33

.. code-block:: Python

    model = ot.SymbolicFunction(["E", "F", "L", "I"], ["F*L^3/(3*E*I)"])








.. GENERATED FROM PYTHON SOURCE LINES 34-35

Define the problems

.. GENERATED FROM PYTHON SOURCE LINES 35-42

.. code-block:: Python

    minProblem = ot.OptimizationProblem(model)
    minProblem.setBounds(bounds)

    maxProblem = ot.OptimizationProblem(model)
    maxProblem.setBounds(bounds)
    maxProblem.setMinimization(False)








.. GENERATED FROM PYTHON SOURCE LINES 43-44

Create a solver

.. GENERATED FROM PYTHON SOURCE LINES 44-47

.. code-block:: Python

    solver = ot.TNC()
    solver.setStartingPoint(distribution.getMean())








.. GENERATED FROM PYTHON SOURCE LINES 48-49

Solve the problems

.. GENERATED FROM PYTHON SOURCE LINES 49-58

.. code-block:: Python

    solver.setProblem(minProblem)
    solver.run()
    minResult = solver.getResult()
    print("min: y=", minResult.getOptimalValue(), "with x=", minResult.getOptimalPoint())

    solver.setProblem(maxProblem)
    solver.run()
    maxResult = solver.getResult()
    print("max: y=", maxResult.getOptimalValue(), "with x=", maxResult.getOptimalPoint())




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

 .. code-block:: none

    min: y= [6.37642] with x= [4.04419e+07,21319.7,251,435.785]
    max: y= [23.4246] with x= [2.87477e+07,41178.7,259,354.141]





.. _sphx_glr_download_auto_numerical_methods_optimization_plot_minmax_optimization.py:

.. only:: html

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

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

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

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

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