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

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

.. _sphx_glr_advanced_mathematical_optimization_auto_examples_plot_constraints.py:


Constraint optimization: visualizing the geometry
==================================================

A small figure explaining optimization with constraints




.. rst-class:: sphx-glr-horizontal


    *

      .. image:: /advanced/mathematical_optimization/auto_examples/images/sphx_glr_plot_constraints_001.png
            :class: sphx-glr-multi-img

    *

      .. image:: /advanced/mathematical_optimization/auto_examples/images/sphx_glr_plot_constraints_002.png
            :class: sphx-glr-multi-img





.. code-block:: python

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

    x, y = np.mgrid[-2.9:5.8:.05, -2.5:5:.05]
    x = x.T
    y = y.T

    for i in (1, 2):
        # Create 2 figure: only the second one will have the optimization
        # path
        plt.figure(i, figsize=(3, 2.5))
        plt.clf()
        plt.axes([0, 0, 1, 1])

        contours = plt.contour(np.sqrt((x - 3)**2 + (y - 2)**2),
                            extent=[-3, 6, -2.5, 5],
                            cmap=plt.cm.gnuplot)
        plt.clabel(contours,
                inline=1,
                fmt='%1.1f',
                fontsize=14)
        plt.plot([-1.5, -1.5,  1.5,  1.5, -1.5],
                [-1.5,  1.5,  1.5, -1.5, -1.5], 'k', linewidth=2)
        plt.fill_between([ -1.5,  1.5],
                        [ -1.5, -1.5],
                        [  1.5,  1.5],
                        color='.8')
        plt.axvline(0, color='k')
        plt.axhline(0, color='k')

        plt.text(-.9, 4.4, '$x_2$', size=20)
        plt.text(5.6, -.6, '$x_1$', size=20)
        plt.axis('equal')
        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)


    # We don't use the gradient, as with the gradient, L-BFGS is too fast,
    # and finds the optimum without showing us a pretty path
    def f_prime(x):
        r = np.sqrt((x[0] - 3)**2 + (x[0] - 2)**2)
        return np.array(((x[0] - 3)/r, (x[0] - 2)/r))

    optimize.minimize(f, np.array([0, 0]), method="L-BFGS-B",
                         bounds=((-1.5, 1.5), (-1.5, 1.5)))

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

    plt.show()

**Total running time of the script:** ( 0 minutes  0.075 seconds)


.. _sphx_glr_download_advanced_mathematical_optimization_auto_examples_plot_constraints.py:


.. only :: html

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



  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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