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

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

.. _sphx_glr_advanced_mathematical_optimization_auto_examples_plot_convex.py:


Convex function
================

A figure showing the definition of a convex function




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


    *

      .. image:: /advanced/mathematical_optimization/auto_examples/images/sphx_glr_plot_convex_001.png
            :class: sphx-glr-multi-img

    *

      .. image:: /advanced/mathematical_optimization/auto_examples/images/sphx_glr_plot_convex_002.png
            :class: sphx-glr-multi-img





.. code-block:: python


    import numpy as np
    import matplotlib.pyplot as plt

    x = np.linspace(-1, 2)

    plt.figure(1, figsize=(3, 2.5))
    plt.clf()

    # A convex function
    plt.plot(x, x**2, linewidth=2)
    plt.text(-.7, -.6**2, '$f$', size=20)

    # The tangent in one point
    plt.plot(x, 2*x - 1)
    plt.plot(1, 1, 'k+')
    plt.text(.3, -.75, "Tangent to $f$", size=15)
    plt.text(1, 1 - .5, 'C', size=15)

    # Convexity as barycenter
    plt.plot([.35, 1.85], [.35**2, 1.85**2])
    plt.plot([.35, 1.85], [.35**2, 1.85**2], 'k+')
    plt.text(.35 - .2, .35**2 + .1, 'A', size=15)
    plt.text(1.85 - .2, 1.85**2, 'B', size=15)

    plt.ylim(ymin=-1)
    plt.axis('off')
    plt.tight_layout()

    # Convexity as barycenter
    plt.figure(2, figsize=(3, 2.5))
    plt.clf()
    plt.plot(x, x**2 + np.exp(-5*(x - .5)**2), linewidth=2)
    plt.text(-.7, -.6**2, '$f$', size=20)

    plt.ylim(ymin=-1)
    plt.axis('off')
    plt.tight_layout()
    plt.show()


**Total running time of the script:** ( 0 minutes  0.064 seconds)


.. _sphx_glr_download_advanced_mathematical_optimization_auto_examples_plot_convex.py:


.. only :: html

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



  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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