:orphan:

Examples for the mathematical optimization chapter
==================================================



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    <div class="sphx-glr-thumbnails">

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    <div class="sphx-glr-thumbcontainer" tooltip="Draws a figure explaining noisy vs non-noisy optimization">

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  .. image:: /advanced/mathematical_optimization/auto_examples/images/thumb/sphx_glr_plot_noisy_thumb.png
    :alt:

  :ref:`sphx_glr_advanced_mathematical_optimization_auto_examples_plot_noisy.py`

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      <div class="sphx-glr-thumbnail-title">Noisy optimization problem</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Draws a figure to explain smooth versus non smooth optimization.">

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  .. image:: /advanced/mathematical_optimization/auto_examples/images/thumb/sphx_glr_plot_smooth_thumb.png
    :alt:

  :ref:`sphx_glr_advanced_mathematical_optimization_auto_examples_plot_smooth.py`

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      <div class="sphx-glr-thumbnail-title">Smooth vs non-smooth</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="A curve fitting example">

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  .. image:: /advanced/mathematical_optimization/auto_examples/images/thumb/sphx_glr_plot_curve_fitting_thumb.png
    :alt:

  :ref:`sphx_glr_advanced_mathematical_optimization_auto_examples_plot_curve_fitting.py`

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      <div class="sphx-glr-thumbnail-title">Curve fitting</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="A figure showing the definition of a convex function">

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  .. image:: /advanced/mathematical_optimization/auto_examples/images/thumb/sphx_glr_plot_convex_thumb.png
    :alt:

  :ref:`sphx_glr_advanced_mathematical_optimization_auto_examples_plot_convex.py`

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      <div class="sphx-glr-thumbnail-title">Convex function</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="An exercise of finding minimum. This exercise is hard because the function is very flat around the minimum (all its derivatives are zero). Thus gradient information is unreliable.">

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  .. image:: /advanced/mathematical_optimization/auto_examples/images/thumb/sphx_glr_plot_exercise_flat_minimum_thumb.png
    :alt:

  :ref:`sphx_glr_advanced_mathematical_optimization_auto_examples_plot_exercise_flat_minimum.py`

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      <div class="sphx-glr-thumbnail-title">Finding a minimum in a flat neighborhood</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="An example showing how to do optimization with general constraints using SLSQP and cobyla.">

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  .. image:: /advanced/mathematical_optimization/auto_examples/images/thumb/sphx_glr_plot_non_bounds_constraints_thumb.png
    :alt:

  :ref:`sphx_glr_advanced_mathematical_optimization_auto_examples_plot_non_bounds_constraints.py`

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      <div class="sphx-glr-thumbnail-title">Optimization with constraints</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Illustration of 1D optimization: Brent&#x27;s method">

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  .. image:: /advanced/mathematical_optimization/auto_examples/images/thumb/sphx_glr_plot_1d_optim_thumb.png
    :alt:

  :ref:`sphx_glr_advanced_mathematical_optimization_auto_examples_plot_1d_optim.py`

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      <div class="sphx-glr-thumbnail-title">Brent's method</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="A small figure explaining optimization with constraints">

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  .. image:: /advanced/mathematical_optimization/auto_examples/images/thumb/sphx_glr_plot_constraints_thumb.png
    :alt:

  :ref:`sphx_glr_advanced_mathematical_optimization_auto_examples_plot_constraints.py`

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      <div class="sphx-glr-thumbnail-title">Constraint optimization: visualizing the geometry</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="The challenge here is that Hessian of the problem is a very ill-conditioned matrix. This can easily be seen, as the Hessian of the first term in simply 2 * K.T @ K. Thus the conditioning of the problem can be judged from looking at the conditioning of K.">

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  .. image:: /advanced/mathematical_optimization/auto_examples/images/thumb/sphx_glr_plot_exercise_ill_conditioned_thumb.png
    :alt:

  :ref:`sphx_glr_advanced_mathematical_optimization_auto_examples_plot_exercise_ill_conditioned.py`

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      <div class="sphx-glr-thumbnail-title">Alternating optimization</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Plots the results from the comparison of optimizers.">

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  .. image:: /advanced/mathematical_optimization/auto_examples/images/thumb/sphx_glr_plot_compare_optimizers_thumb.png
    :alt:

  :ref:`sphx_glr_advanced_mathematical_optimization_auto_examples_plot_compare_optimizers.py`

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      <div class="sphx-glr-thumbnail-title">Plotting the comparison of optimizers</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="An example demoing gradient descent by creating figures that trace the evolution of the optimizer.">

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  .. image:: /advanced/mathematical_optimization/auto_examples/images/thumb/sphx_glr_plot_gradient_descent_thumb.png
    :alt:

  :ref:`sphx_glr_advanced_mathematical_optimization_auto_examples_plot_gradient_descent.py`

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      <div class="sphx-glr-thumbnail-title">Gradient descent</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /advanced/mathematical_optimization/auto_examples/plot_noisy
   /advanced/mathematical_optimization/auto_examples/plot_smooth
   /advanced/mathematical_optimization/auto_examples/plot_curve_fitting
   /advanced/mathematical_optimization/auto_examples/plot_convex
   /advanced/mathematical_optimization/auto_examples/plot_exercise_flat_minimum
   /advanced/mathematical_optimization/auto_examples/plot_non_bounds_constraints
   /advanced/mathematical_optimization/auto_examples/plot_1d_optim
   /advanced/mathematical_optimization/auto_examples/plot_constraints
   /advanced/mathematical_optimization/auto_examples/plot_exercise_ill_conditioned
   /advanced/mathematical_optimization/auto_examples/plot_compare_optimizers
   /advanced/mathematical_optimization/auto_examples/plot_gradient_descent


.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-gallery

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download all examples in Python source code: auto_examples_python.zip </advanced/mathematical_optimization/auto_examples/auto_examples_python.zip>`

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

      :download:`Download all examples in Jupyter notebooks: auto_examples_jupyter.zip </advanced/mathematical_optimization/auto_examples/auto_examples_jupyter.zip>`


.. only:: html

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

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