.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/plot_example4.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_examples_plot_example4.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_plot_example4.py:


Example 4
=========

.. GENERATED FROM PYTHON SOURCE LINES 7-21

Problem statement:

.. math::

    \begin{aligned}
    & \underset{x}{\text{minimize}}
    & & \mathbb{E}_{\cD}(\cos(x) \sin(\Theta)) \\
    & \text{subject to}
    & & \mathbb{P}_{\cD}(-2 - x + \Theta \leq 0) \geq 0.9 \\
    & & & x - 4 \leq 0 \\
    & & & \Theta \thicksim \cU(0, 2)
    \end{aligned}

Solution: :math:`\hat{x} = \pi`

.. GENERATED FROM PYTHON SOURCE LINES 23-54

.. code-block:: Python

    import openturns as ot
    import otrobopt

    # ot.Log.Show(ot.Log.Info)

    calJ = ot.SymbolicFunction(['x', 'theta'], ['cos(x) * sin(theta)'])
    calG = ot.SymbolicFunction(['x', 'theta'], ['-(-2 - x + theta)', '-(x - 4)'])
    J = ot.ParametricFunction(calJ, [1], [1.0])
    g = ot.ParametricFunction(calG, [1], [1.0])

    dim = J.getInputDimension()

    solver = ot.Cobyla()
    solver.setMaximumIterationNumber(1000)
    solver.setStartingPoint([0.0] * dim)

    thetaDist = ot.Uniform(0.0, 2.0)
    robustnessMeasure = otrobopt.MeanMeasure(J, thetaDist)
    reliabilityMeasure = otrobopt.JointChanceMeasure(
        g, thetaDist, ot.Greater(), 0.9)
    problem = otrobopt.RobustOptimizationProblem(
        robustnessMeasure, reliabilityMeasure)

    algo = otrobopt.SequentialMonteCarloRobustAlgorithm(problem, solver)
    algo.setMaximumIterationNumber(10)
    algo.setMaximumAbsoluteError(1e-3)
    algo.setInitialSamplingSize(10)
    algo.run()
    result = algo.getResult()
    print('x*=', result.getOptimalPoint(), 'J(x*)=',
          result.getOptimalValue(), 'iteration=', result.getIterationNumber())




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

 .. code-block:: none

    x*= [3.14159] J(x*)= [-0.757706] iteration= 2





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

   **Total running time of the script:** (0 minutes 0.007 seconds)


.. _sphx_glr_download_auto_examples_plot_example4.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_example4.ipynb <plot_example4.ipynb>`

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

      :download:`Download Python source code: plot_example4.py <plot_example4.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_example4.zip <plot_example4.zip>`