:orphan:

.. _examples:

Examples
========

This section provides several examples of how to use **csnlp**. It ranges from the
basic, e.g., how to build an NLP with :class:`csnlp.Nlp`, to more advanced examples that
showcase, e.g., how to use the :mod:`csnlp.multistart` submodule.

.. _introductory_examples:

Introductory examples
---------------------

General-purpose and introductory examples for :mod:`csnlp`.



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    <div class="sphx-glr-thumbcontainer" tooltip="Again, this example illustrates another simple use of csnlp.Nlp in solving an optimization problem.">

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  .. image:: /auto_examples/images/thumb/sphx_glr_chain_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_chain.py`

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      <div class="sphx-glr-thumbnail-title">A simple optimization problem: hanging chain</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the basic usage of csnlp.Nlp in solving a simple optimization problem, taken from this CasADi blog post">

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  .. image:: /auto_examples/images/thumb/sphx_glr_rosenbrock_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_rosenbrock.py`

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      <div class="sphx-glr-thumbnail-title">A simple optimization problem: Rosenbrock function</div>
    </div>


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.. toctree::
   :hidden:

   /auto_examples/chain
   /auto_examples/rosenbrock


Integer Programming examples
--------------------------------

Here we show how to specify discrete and binary domains for variables.



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    <div class="sphx-glr-thumbcontainer" tooltip="In this example, we show how to formualte and solve a simple mixed integer linear programming (MILP) problem via csnlp. This simple problem, taken from here, is">

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  .. image:: /auto_examples/integer-programming/images/thumb/sphx_glr_milp_and_miqp_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_integer-programming_milp_and_miqp.py`

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      <div class="sphx-glr-thumbnail-title">A mixed integer linear programming example</div>
    </div>


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    </div>


Multistart Optimization examples
--------------------------------

The following examples demonstrate the use of :mod:`csnlp.multistart` to combat local
convergence.



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    <div class="sphx-glr-thumbcontainer" tooltip="In this example, we show how to solve a simple nonlinear optimization problem with multiple minimas using the multistart capabilities of csnlp.multistart.">

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  .. image:: /auto_examples/multistart/images/thumb/sphx_glr_nlp_with_multistart_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_multistart_nlp_with_multistart.py`

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      <div class="sphx-glr-thumbnail-title">A simple problem with multiple minima</div>
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Optimal control examples
------------------------

These examples detail how to use :mod:`csnlp` to create and solve optimal control
problems with :class:`csnlp.wrappers.Mpc`, :class:`csnlp.wrappers.ScenarioBasedMpc`, and
other similar wrapper classes.



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    <div class="sphx-glr-thumbcontainer" tooltip="This example demos how an MPC controller can be built via csnlp.wrappers.Mpc and how it can be solved in an open-loop fashion.">

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  .. image:: /auto_examples/optimal_control/images/thumb/sphx_glr_open_loop_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_optimal_control_open_loop.py`

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      <div class="sphx-glr-thumbnail-title">Simple open-loop MPC controller</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This example demos how an MPC controller can be built for a linear system using csnlp.wrappers.Mpc and its csnlp.wrappers.Mpc.set_affine_dynamics method. The system is a simple linear system with the following dynamics:">

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  .. image:: /auto_examples/optimal_control/images/thumb/sphx_glr_linear_mpc_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_optimal_control_linear_mpc.py`

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      <div class="sphx-glr-thumbnail-title">Linear MPC control</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This example shows how to use the csnlp.wrappers.MultiScenarioMpc to create a multi-scenario MPC controller. We will only solve it once to demonstrate its open-loop solution, but of course the controller can and should be used in a receding horizon fashion, as done in the other examples. It is highly recommended to first go through the example scenario_based_mpc_example to familiarize yourself with csnlp.wrappers.ScenarioBasedMpc.">

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  .. image:: /auto_examples/optimal_control/images/thumb/sphx_glr_mpc_multiple_scenarios_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_optimal_control_mpc_multiple_scenarios.py`

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      <div class="sphx-glr-thumbnail-title">Multiple Scenario MPC</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="In this example, we demonstrate how to build a scenario-based model predictive control (SCMPC) using csnlp.wrappers.ScenarioBasedMpc. The problem is inspired by the numerical results of schildbach_scenario_2014 shown in Tables 1 and 2, for R = R_1 = R_2 = 0.">

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  .. image:: /auto_examples/optimal_control/images/thumb/sphx_glr_scenario_approach_for_mpc_thumb.png
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  :ref:`sphx_glr_auto_examples_optimal_control_scenario_approach_for_mpc.py`

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      <div class="sphx-glr-thumbnail-title">Scenario-based MPC</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example demos how an MPC controller can be built for a simple system with piecewise affine dynamics using csnlp.wrappers.PwaMpc. We assume some knowledge of MPC is already present; otherwise, refer to other optimal control examples. For more details on the subject of control for PWA and hybrid systems , see bemporad_control_1999 and borrelli_predictive_2017.">

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  .. image:: /auto_examples/optimal_control/images/thumb/sphx_glr_mpc_for_pwa_system_thumb.png
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  :ref:`sphx_glr_auto_examples_optimal_control_mpc_for_pwa_system.py`

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      <div class="sphx-glr-thumbnail-title">MPC controller for PWA systems</div>
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Scaling examples
----------------

Examples demonstrating the scaling capabilities of :class:`csnlp.wrappers.NlpScaling`.



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    <div class="sphx-glr-thumbcontainer" tooltip="This example showcases a optimal control task where the scaling of the NLP variables can really impact the performance of the solver. This is due to the fact that the variables have widely different scales, making it challenging for the solver to find a good numerical solutions.">

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  .. image:: /auto_examples/scaling/images/thumb/sphx_glr_nlp_scaling_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_scaling_nlp_scaling.py`

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      <div class="sphx-glr-thumbnail-title">How scaling can help convergence</div>
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Sensitivity examples
--------------------

Examples on sensitivity computations via :class:`csnlp.wrappers.NlpSensitivity`.



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    <div class="sphx-glr-thumbcontainer" tooltip="In this example we explore the parametric sensitivity of an NLP problem. We will use the csnlp.wrappers.NlpSensitivity wrapper to achieve so, but we&#x27;ll skip over some of the formalities of the library, as we assume you are already a bit familiar with it. If this is not the case, for more introductory examples on csnlp, see the other introductory_examples.">

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  .. image:: /auto_examples/sensitivity/images/thumb/sphx_glr_simple_sensitivity_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_sensitivity_simple_sensitivity.py`

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      <div class="sphx-glr-thumbnail-title">A simple example of sensitivity analysis</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example builts on top of the example simple_sensitivity_example and extends it to a 3d setting, i.e., we consider the sensitivities w.r.t. both parameters. Not much else changes, so comments are sparse for brevity. For referece, the NLP here considered is">

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  .. image:: /auto_examples/sensitivity/images/thumb/sphx_glr_simple_sensitivity_3d_thumb.png
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  :ref:`sphx_glr_auto_examples_sensitivity_simple_sensitivity_3d.py`

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      <div class="sphx-glr-thumbnail-title">A simple example of sensitivity analysis (3d version)</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="In this example, we reproduce the sensitivity computations from this CasADi example, both with casadi&#x27;s native capabilities as well as the one from csnlp.">

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  .. image:: /auto_examples/sensitivity/images/thumb/sphx_glr_comparison_sensitivities_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_sensitivity_comparison_sensitivities.py`

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      <div class="sphx-glr-thumbnail-title">Comparison of CasADi's and csnlp's sensitivity computations</div>
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.. toctree::
   :hidden:
   :includehidden:


   /auto_examples/integer-programming/index.rst
   /auto_examples/multistart/index.rst
   /auto_examples/optimal_control/index.rst
   /auto_examples/scaling/index.rst
   /auto_examples/sensitivity/index.rst


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  .. 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 </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 </auto_examples/auto_examples_jupyter.zip>`


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