.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_numerical_methods_optimization_plot_optimization_nlopt.py>`     to download the full example code
    .. rst-class:: sphx-glr-example-title

    .. _sphx_glr_auto_numerical_methods_optimization_plot_optimization_nlopt.py:


Optimization using NLopt
========================

In this example we are going to explore optimization using OpenTURNS' `NLopt <https://nlopt.readthedocs.io/en/latest/>`_ interface.


.. 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)








List available algorithms


.. code-block:: default

    for algo in ot.NLopt.GetAlgorithmNames():
        print(algo)





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

 Out:

 .. code-block:: none

    AUGLAG
    AUGLAG_EQ
    GD_MLSL
    GD_MLSL_LDS
    GN_CRS2_LM
    GN_DIRECT
    GN_DIRECT_L
    GN_DIRECT_L_NOSCAL
    GN_DIRECT_L_RAND
    GN_DIRECT_L_RAND_NOSCAL
    GN_DIRECT_NOSCAL
    GN_ESCH
    GN_ISRES
    GN_MLSL
    GN_MLSL_LDS
    GN_ORIG_DIRECT
    GN_ORIG_DIRECT_L
    G_MLSL
    G_MLSL_LDS
    LD_AUGLAG
    LD_AUGLAG_EQ
    LD_CCSAQ
    LD_LBFGS
    LD_MMA
    LD_SLSQP
    LD_TNEWTON
    LD_TNEWTON_PRECOND
    LD_TNEWTON_PRECOND_RESTART
    LD_TNEWTON_RESTART
    LD_VAR1
    LD_VAR2
    LN_AUGLAG
    LN_AUGLAG_EQ
    LN_BOBYQA
    LN_COBYLA
    LN_NELDERMEAD
    LN_NEWUOA
    LN_NEWUOA_BOUND
    LN_PRAXIS
    LN_SBPLX




More details on NLopt algorithms are available `here <https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/>`_ .

The optimization algorithm is instanciated from the NLopt name


.. code-block:: default

    algo = ot.NLopt('LD_SLSQP')








define the problem


.. code-block:: default

    objective = ot.SymbolicFunction(['x1', 'x2'], ['100*(x2-x1^2)^2+(1-x1)^2'])
    inequality_constraint = ot.SymbolicFunction(['x1', 'x2'], ['x1-2*x2'])
    dim = objective.getInputDimension()
    bounds = ot.Interval([-3.] * dim, [5.] * dim)
    problem = ot.OptimizationProblem(objective)
    problem.setMinimization(True)
    problem.setInequalityConstraint(inequality_constraint)
    problem.setBounds(bounds)








solve the problem


.. code-block:: default

    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^= [0.517441,0.258721]




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_nlopt_001.png
    :alt: Optimal value history
    :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  0.083 seconds)


.. _sphx_glr_download_auto_numerical_methods_optimization_plot_optimization_nlopt.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_nlopt.py <plot_optimization_nlopt.py>`



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

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


.. only:: html

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

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