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Welcome to CVXPY 1.9
====================

.. meta::
   :description: An open source Python-embedded modeling language for convex optimization problems.
                 Express your problem in a natural way that follows the math.
   :keywords: convex optimization, open source, software,

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**Convex optimization, for everyone.**

*Help us benchmark CVXPY solvers! Contribute problems and results to the* `Solver Benchmarks <resources/solver_benchmarks/>`_ *project.*
*We are building a CVXPY community* `on Discord <https://discord.gg/4urRQeGBCr>`_. *Join the conversation!*

CVXPY is an open source Python-embedded modeling language for convex
optimization problems. It lets you express your problem in a natural way that
follows the math, rather than in the restrictive standard form required by
solvers.

For example, the following code solves a least-squares problem with box constraints:

.. code:: python

    import cvxpy as cp
    import numpy as np

    # Problem data.
    m = 30
    n = 20
    np.random.seed(1)
    A = np.random.randn(m, n)
    b = np.random.randn(m)

    # Construct the problem.
    x = cp.Variable(n)
    objective = cp.Minimize(cp.sum_squares(A @ x - b))
    constraints = [0 <= x, x <= 1]
    prob = cp.Problem(objective, constraints)

    # The optimal objective value is returned by `prob.solve()`.
    result = prob.solve()
    # The optimal value for x is stored in `x.value`.
    print(x.value)
    # The optimal Lagrange multiplier for a constraint is stored in
    # `constraint.dual_value`.
    print(constraints[0].dual_value)

This short script is a basic example of what CVXPY can do. In addition
to convex programming, CVXPY also supports :doc:`parametrized programming </tutorial/dpp/index>`,
:doc:`geometric programming </tutorial/dgp/index>`, :ref:`mixed-integer convex programs <mip>`,
:doc:`quasiconvex programming </tutorial/dqcp/index>`,
and :doc:`nonlinear programming </tutorial/dnlp/index>`.

For a guided tour of CVXPY, check out the :doc:`tutorial
</tutorial/index>`. For applications to machine learning, control, finance, and
more, browse the :doc:`library of examples </examples/index>`.
For applications that involve nonlinear programming, visit the
`library of DNLP examples <https://github.com/cvxgrp/dnlp-examples/>`_.
For background on convex optimization, see the book `Convex Optimization
<https://www.stanford.edu/~boyd/cvxbook/>`_ by Boyd and Vandenberghe.

CVXPY relies on the open source solvers `Clarabel`_, `OSQP`_, `SCS`_, `HIGHS`_.
Additional solvers are supported, but must be installed separately.

**Community.**

The CVXPY community consists of researchers, data scientists, software
engineers, and students from all over the world. We welcome you to join us!

* To chat with the CVXPY community in real-time, join us `on Discord <https://discord.gg/4urRQeGBCr>`_.

* To have longer, in-depth discussions with the CVXPY community, use `Github discussions <https://github.com/cvxpy/cvxpy/discussions>`_.

* To share feature requests and bug reports, use the `issue tracker <https://github.com/cvxpy/cvxpy/issues>`_.

**Development.**

CVXPY is a community project, built from the contributions of many
researchers and engineers.

CVXPY is developed and maintained by
`Steven Diamond <https://stevendiamond.me/>`_,
`Riley Murray <https://rileyjmurray.wordpress.com/>`_,
`Philipp Schiele <https://www.philippschiele.com/>`_,
`Parth Nobel <https://ptnobel.github.io/>`_, and
`William Zhang <https://zijie.ca/>`_.
CVXPY's emeritus maintainers are
`Bartolomeo Stellato <https://stellato.io/>`_ and `Akshay Agrawal <https://akshayagrawal.com>`_.
Many others have contributed significantly.
A non-exhaustive list of people who have shaped CVXPY over the
years includes Stephen Boyd, Eric Chu, Robin Verschueren,
Jaehyun Park, Enzo Busseti, AJ Friend, Judson Wilson, Chris Dembia, and Daniel Cederberg.

We appreciate all contributions. To get involved, see our :doc:`contributing
guide </contributing/index>` and join us `on Discord <https://discord.gg/4urRQeGBCr>`_.

**News.**

CVXPY 1.9 introduces *Disciplined Nonlinear Programming* (DNLP), a grammar
for specifying nonlinear programs (NLP) which extends CVXPY beyond convex optimization.
CVXPY currently supports four NLP solvers:
`IPOPT <https://github.com/coin-or/Ipopt>`_,
`KNITRO <https://www.artelys.com/solvers/knitro/>`_,
`UNO <https://github.com/cvanaret/Uno>`_, and
`COPT <https://www.shanshu.ai/copt>`_.
For a complete list of changes, see the :doc:`changelog </updates/index>`.

.. _Clarabel: https://github.com/oxfordcontrol/Clarabel.rs
.. _OSQP: https://osqp.org/
.. _SCS: http://github.com/cvxgrp/scs
.. _HIGHS: https://github.com/ERGO-Code/HiGHS

.. toctree::
   :hidden:

   install/index

.. toctree::
    :hidden:

    User Guide <tutorial/index>

.. toctree::
   :hidden:

   functions/index

.. toctree::
   :hidden:

   API Documentation <api_reference/cvxpy>

.. toctree::
   :hidden:

   examples/index

.. toctree::
   :hidden:

   contributing/index

.. toctree::
   :hidden:

   Changelog <updates/index>

.. toctree::
   :maxdepth: 1
   :hidden:

   faq/index

.. toctree::
   :hidden:

   resources/index

.. toctree::
   :hidden:

   workshop/index