.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/optimization_problem/plot_simple_opt_1.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        Click :ref:`here <sphx_glr_download_examples_optimization_problem_plot_simple_opt_1.py>`
        to download the full example code

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

.. _sphx_glr_examples_optimization_problem_plot_simple_opt_1.py:


Analytical test case # 1
========================

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In this example, we consider a simple optimization problem to illustrate
algorithms interfaces and :class:`.MDOFunction`.

Imports
-----------------------------

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.. code-block:: default

    from __future__ import division, unicode_literals

    from numpy import cos, exp, ones, sin
    from scipy import optimize

    from gemseo.api import configure_logger
    from gemseo.core.mdofunctions.mdo_function import MDOFunction

    configure_logger()






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

 Out:

 .. code-block:: none


    <RootLogger root (INFO)>



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Define the objective function
-----------------------------
We define the objective function :math:`f(x)=sin(x)-exp(x)`
using a :class:`.MDOFunction` defined by the sum of :class:`.MDOFunction` s.

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.. code-block:: default


    f_1 = MDOFunction(sin, name="f_1", jac=cos, expr="sin(x)")
    f_2 = MDOFunction(exp, name="f_2", jac=exp, expr="exp(x)")
    objective = f_1 - f_2








.. GENERATED FROM PYTHON SOURCE LINES 55-60

.. seealso::

   The following operators are implemented: :math:`+`, :math:`-`
   and :math:`*`. The minus operator is also defined.


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.. code-block:: default


    print("Objective function = ", objective)





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

 Out:

 .. code-block:: none

    Objective function =  f_1-f_2 = sin(x)-exp(x)




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Minimize the objective function
-------------------------------
We want to minimize this objective function over :math:`[-2,2]`,
starting from 1.
We use scipy.optimize for illustration.

.. note::

   :class:`.MDOFunction` objects are callable like a Python function.


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.. code-block:: default


    x_0 = -ones(1)
    opt = optimize.fmin_l_bfgs_b(objective, x_0, fprime=objective.jac, bounds=[(-0.2, 2.0)])

    print("Optimum = ", opt)




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

 Out:

 .. code-block:: none

    Optimum =  (array([-0.2]), array([-1.01740008]), {'grad': array([0.16133582]), 'task': 'CONVERGENCE: NORM_OF_PROJECTED_GRADIENT_<=_PGTOL', 'funcalls': 1, 'nit': 0, 'warnflag': 0})





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

   **Total running time of the script:** ( 0 minutes  0.003 seconds)


.. _sphx_glr_download_examples_optimization_problem_plot_simple_opt_1.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_simple_opt_1.py <plot_simple_opt_1.py>`



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

     :download:`Download Jupyter notebook: plot_simple_opt_1.ipynb <plot_simple_opt_1.ipynb>`


.. only:: html

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

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