A domain-specific language for modeling convex optimization problems in Python.

CVXPY

The CVXPY documentation is at cvxpy.org.

We are building a CVXPY community on Discord. Join the conversation! For issues and long-form discussions, use Github Issues and Github Discussions.

Contents

CVXPY is a Python-embedded modeling language for convex optimization problems. It allows you to 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 where the variable is constrained by lower and upper bounds:

import cvxpy as cp
import numpy

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


With CVXPY, you can model

• convex optimization problems,
• mixed-integer convex optimization problems,
• geometric programs, and
• quasiconvex programs.

CVXPY is not a solver. It relies upon the open source solvers Clarabel, ECOS, SCS, and OSQP. Additional solvers are available, but must be installed separately.

CVXPY began as a Stanford University research project. It is now developed by many people, across many institutions and countries.

Installation

CVXPY is available on PyPI, and can be installed with

pip install cvxpy


CVXPY can also be installed with conda, using

conda install -c conda-forge cvxpy


CVXPY has the following dependencies:

• Python >= 3.8
• Clarabel >= 0.5.0
• OSQP >= 0.6.2
• ECOS >= 2
• SCS >= 3.2.4.post1
• NumPy >= 1.15
• SciPy >= 1.1.0

For detailed instructions, see the installation guide.

Getting started

To get started with CVXPY, check out the following:

Issues

We encourage you to report issues using the Github tracker. We welcome all kinds of issues, especially those related to correctness, documentation, performance, and feature requests.

For basic usage questions (e.g., "Why isn't my problem DCP?"), please use StackOverflow instead.

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.
• To have longer, in-depth discussions with the CVXPY community, use Github Discussions.
• To share feature requests and bug reports, use Github Issues.

Please be respectful in your communications with the CVXPY community, and make sure to abide by our code of conduct.

Contributing

We appreciate all contributions. You don't need to be an expert in convex optimization to help out.

You should first install CVXPY from source. Here are some simple ways to start contributing immediately:

If you'd like to add a new example to our library, or implement a new feature, please get in touch with us first to make sure that your priorities align with ours.

Contributions should be submitted as pull requests. A member of the CVXPY development team will review the pull request and guide you through the contributing process.

Team

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

CVXPY is developed and maintained by Steven Diamond, Akshay Agrawal, Riley Murray, Philipp Schiele, and Bartolomeo Stellato, 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 Parth Nobel.

Citing

If you use CVXPY for academic work, we encourage you to cite our papers. If you use CVXPY in industry, we'd love to hear from you as well, on Discord or over email.

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