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

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

.. _sphx_glr_advanced_mathematical_optimization_auto_examples_plot_non_bounds_constraints.py:


Optimization with constraints
================================

An example showing how to do optimization with general constraints using
SLSQP and cobyla.




.. image:: /advanced/mathematical_optimization/auto_examples/images/sphx_glr_plot_non_bounds_constraints_001.png
    :class: sphx-glr-single-img





.. code-block:: python

    import numpy as np
    import matplotlib.pyplot as plt
    from scipy import optimize

    x, y = np.mgrid[-2.03:4.2:.04, -1.6:3.2:.04]
    x = x.T
    y = y.T

    plt.figure(1, figsize=(3, 2.5))
    plt.clf()
    plt.axes([0, 0, 1, 1])

    contours = plt.contour(np.sqrt((x - 3)**2 + (y - 2)**2),
                        extent=[-2.03, 4.2, -1.6, 3.2],
                        cmap=plt.cm.gnuplot)
    plt.clabel(contours,
            inline=1,
            fmt='%1.1f',
            fontsize=14)
    plt.plot([-1.5,    0,  1.5,    0, -1.5],
            [   0,  1.5,    0, -1.5,    0], 'k', linewidth=2)
    plt.fill_between([ -1.5,    0,  1.5],
                    [    0, -1.5,    0],
                    [    0,  1.5,    0],
                    color='.8')
    plt.axvline(0, color='k')
    plt.axhline(0, color='k')

    plt.text(-.9, 2.8, '$x_2$', size=20)
    plt.text(3.6, -.6, '$x_1$', size=20)
    plt.axis('tight')
    plt.axis('off')

    # And now plot the optimization path
    accumulator = list()

    def f(x):
        # Store the list of function calls
        accumulator.append(x)
        return np.sqrt((x[0] - 3)**2 + (x[1] - 2)**2)


    def constraint(x):
        return np.atleast_1d(1.5 - np.sum(np.abs(x)))

    optimize.minimize(f, np.array([0, 0]), method="SLSQP",
                         constraints={"fun": constraint, "type": "ineq"})

    accumulated = np.array(accumulator)
    plt.plot(accumulated[:, 0], accumulated[:, 1])

    plt.show()

**Total running time of the script:** ( 0 minutes  0.040 seconds)


.. _sphx_glr_download_advanced_mathematical_optimization_auto_examples_plot_non_bounds_constraints.py:


.. only :: html

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



  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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