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Welcome to CVXPY 1.9

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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 inviting CVXPY users to share their experience with the library and their application area so we can better serve you! Sign up for a listening session! <https://calendar.app.google/mRGBur1ZVMW1dcbR8>. 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/>, Akshay Agrawal <https://akshayagrawal.com>, Riley Murray <https://rileyjmurray.wordpress.com/>, Philipp Schiele <https://www.philippschiele.com/>, Bartolomeo Stellato <https://stellato.io/>, and Parth Nobel <https://ptnobel.github.io/> with many others contributing 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 William Zhang.

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

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User Guide <tutorial/index>

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functions/index

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API Documentation <api_reference/cvxpy>

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examples/index

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contributing/index

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Changelog <updates/index>

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faq/index

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resources/index

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workshop/index