qpsolvers

Quadratic programming solvers in Python with a unified API

https://github.com/qpsolvers/qpsolvers

Science Score: 54.0%

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Keywords

numerical-optimization optimization python quadratic-programming solver

Last synced: 4 months ago · JSON representation ·

Repository

Quadratic programming solvers in Python with a unified API

Basic Info

Host: GitHub
Owner: qpsolvers
License: lgpl-3.0
Language: Python
Default Branch: main
Homepage:
Size: 5.28 MB

Statistics

Stars: 685
Watchers: 13
Forks: 98
Open Issues: 10
Releases: 53

Topics

numerical-optimization optimization python quadratic-programming solver

Created over 9 years ago · Last pushed 5 months ago

Metadata Files

Readme Changelog Contributing License Citation

Quadratic Programming Solvers in Python

This library provides a solve_qp function to solve convex quadratic programs:

$$ \begin{split} \begin{array}{ll} \underset{x}{\mbox{minimize}} & \frac{1}{2} x^T P x + q^T x \ \mbox{subject to} & G x \leq h \ & A x = b \ & lb \leq x \leq ub \end{array} \end{split} $$

Vector inequalities apply coordinate by coordinate. The function returns the primal solution $x^*$ found by the backend QP solver, or None in case of failure/unfeasible problem. All solvers require the problem to be convex, meaning the matrix $P$ should be positive semi-definite. Some solvers further require the problem to be strictly convex, meaning $P$ should be positive definite.

Dual multipliers: there is also a solve_problem function that returns not only the primal solution, but also its dual multipliers and all other relevant quantities computed by the backend solver.

Example

To solve a quadratic program, build the matrices that define it and call solve_qp, selecting the backend QP solver via the solver keyword argument:

```python import numpy as np from qpsolvers import solve_qp

M = np.array([[1.0, 2.0, 0.0], [-8.0, 3.0, 2.0], [0.0, 1.0, 1.0]]) P = M.T @ M # this is a positive definite matrix q = np.array([3.0, 2.0, 3.0]) @ M G = np.array([[1.0, 2.0, 1.0], [2.0, 0.0, 1.0], [-1.0, 2.0, -1.0]]) h = np.array([3.0, 2.0, -2.0]) A = np.array([1.0, 1.0, 1.0]) b = np.array([1.0])

x = solve_qp(P, q, G, h, A, b, solver="proxqp") print(f"QP solution: {x = }") ```

This example outputs the solution [0.30769231, -0.69230769, 1.38461538]. It is also possible to get dual multipliers at the solution, as shown in this example.

Installation

From conda-forge

console conda install -c conda-forge qpsolvers

From PyPI

To install the library with open source QP solvers:

console pip install qpsolvers[open_source_solvers]

This one-size-fits-all installation may not work immediately on all systems (for instance if a solver tries to compile from source). If you run into any issue, check out the following variants:

pip install qpsolvers[wheels_only] will only install solvers with pre-compiled binaries,
pip install qpsolvers[clarabel,daqp,proxqp,scs] (for instance) will install the listed set of QP solvers,
pip install qpsolvers will only install the library itself.

When imported, qpsolvers loads all the solvers it can find and lists them in qpsolvers.available_solvers.

Solvers

| Solver | Keyword | Algorithm | API | License | | ------ | ------- | --------- | --- | ------- | | Clarabel | clarabel | Interior point | Sparse | Apache-2.0 | | CVXOPT | cvxopt | Interior point | Dense | GPL-3.0 | | DAQP | daqp | Active set | Dense | MIT | | ECOS | ecos | Interior point | Sparse | GPL-3.0 | | Gurobi | gurobi | Interior point | Sparse | Commercial | | HiGHS | highs | Active set | Sparse | MIT | | HPIPM | hpipm | Interior point | Dense | BSD-2-Clause | | jaxopt.OSQP | jaxopt_osqp | Augmented Lagrangian | Dense | Apache-2.0 | | KVXOPT | kvxopt | Interior point | Dense & Sparse | GPL-3.0 | | MOSEK | mosek | Interior point | Sparse | Commercial | | NPPro | nppro | Active set | Dense | Commercial | | OSQP | osqp | Augmented Lagrangian | Sparse | Apache-2.0 | | PIQP | piqp | Proximal interior point | Dense & Sparse | BSD-2-Clause | | ProxQP | proxqp | Augmented Lagrangian | Dense & Sparse | BSD-2-Clause | | QPALM | qpalm | Augmented Lagrangian | Sparse | LGPL-3.0 | | qpax | qpax | Interior point | Dense | MIT | | qpOASES | qpoases | Active set | Dense | LGPL-2.1 | | qpSWIFT | qpswift | Interior point | Sparse | GPL-3.0 | | quadprog | quadprog | Active set | Dense | GPL-2.0 | | SCS | scs | Augmented Lagrangian | Sparse | MIT | | SIP | sip | Barrier Augmented Lagrangian | Sparse | MIT |

Matrix arguments are NumPy arrays for dense solvers and SciPy Compressed Sparse Column (CSC) matrices for sparse ones.

Frequently Asked Questions

Benchmark

QP solvers come with their strengths and weaknesses depending on the algorithmic choices they make. To help you find the ones most suited to your problems, you can check out the results from qpbenchmark, a benchmark for QP solvers in Python. The benchmark is divided into test sets, each test set representing a different distribution of quadratic programs with specific dimensions and structure (large sparse problems, optimal control problems, ...):

📈 Free-for-all test set: open to all problems submitted by the community.
📈 Maros-Meszaros test set: hard problems curated by the numerical optimization community.
📈 MPC test set: convex model predictive control problems arising in robotics.

Citing qpsolvers

If you find this project useful, please consider giving it a :star: or citing it if your work is scientific:

bibtex @software{qpsolvers, title = {{qpsolvers: Quadratic Programming Solvers in Python}}, author = {Caron, Stéphane and Arnström, Daniel and Bonagiri, Suraj and Dechaume, Antoine and Flowers, Nikolai and Heins, Adam and Ishikawa, Takuma and Kenefake, Dustin and Mazzamuto, Giacomo and Meoli, Donato and O'Donoghue, Brendan and Oppenheimer, Adam A. and Pandala, Abhishek and Quiroz Omaña, Juan José and Rontsis, Nikitas and Shah, Paarth and St-Jean, Samuel and Vitucci, Nicola and Wolfers, Soeren and Yang, Fengyu and @bdelhaisse and @MeindertHH and @rimaddo and @urob and @shaoanlu and Khalil, Ahmed and Kozlov, Lev and Groudiev, Antoine and Sousa Pinto, João and Schwan, Roland and Budhiraja, Rohan}, license = {LGPL-3.0}, url = {https://github.com/qpsolvers/qpsolvers}, version = {4.8.1}, year = {2025} }

Don't forget to add yourself to the BibTeX above and to CITATION.cff if you contribute to this repository.

Contributing

We welcome contributions! The first step is to install the library and use it. Report any bug in the issue tracker. If you're a developer looking to hack on open source, check out the contribution guidelines for suggestions.

cff-version: 1.2.0
message: "If you find this code helpful, please cite it as below."
title: "qpsolvers: Quadratic Programming Solvers in Python"
version: 4.8.1
date-released: 2025-08-07
url: "https://github.com/qpsolvers/qpsolvers"
license: "LGPL-3.0"
authors:
- family-names: "Caron"
  given-names: "Stéphane"
  orcid: "https://orcid.org/0000-0003-2906-692X"
- family-names: "Arnström"
  given-names: "Daniel"
- family-names: "Bonagiri"
  given-names: "Suraj"
- family-names: "Dechaume"
  given-names: "Antoine"
- family-names: "Flowers"
  given-names: "Nikolai"
- family-names: "Heins"
  given-names: "Adam"
- family-names: "Ishikawa"
  given-names: "Takuma"
- family-names: "Kenefake"
  given-names: "Dustin"
- family-names: "Mazzamuto"
  given-names: "Giacomo"
- family-names: "Meoli"
  given-names: "Donato"
- family-names: "O'Donoghue"
  given-names: "Brendan"
- family-names: "Oppenheimer"
  given-names: "Adam A."
- family-names: "Pandala"
  given-names: "Abhishek"
- family-names: "Quiroz Omaña"
  given-names: "Juan José"
- family-names: "Rontsis"
  given-names: "Nikitas"
- family-names: "Shah"
  given-names: "Paarth"
- family-names: "St-Jean"
  given-names: "Samuel"
- family-names: "Vitucci"
  given-names: "Nicola"
- family-names: "Wolfers"
  given-names: "Soeren"
- family-names: "Yang"
  given-names: "Fengyu"
- family-names: "@bdelhaisse"
- family-names: "@MeindertHH"
- family-names: "@rimaddo"
- family-names: "@urob"
- family-names: "@shaoanlu"
- family-names: "Khalil"
  given-names: "Ahmed"
- family-names: "Kozlov"
  given-names: "Lev"
- family-names: "Groudiev"
  given-names: "Antoine"
- family-names: "Sousa Pinto"
  given-names: "João"
  orcid: "https://orcid.org/0000-0003-2469-2809"
- family-names: "Rey"
  given-names: "Valérian"
- family-names: "Schwan"
  given-names: "Roland"
- family-names: "Budhiraja"
  given-names: "Rohan"

GitHub Events

Total

Create event: 17
Release event: 5
Issues event: 10
Watch event: 91
Delete event: 11
Issue comment event: 36
Push event: 88
Pull request review comment event: 7
Pull request review event: 11
Pull request event: 31
Fork event: 8

Last Year

Create event: 17
Release event: 5
Issues event: 10
Watch event: 91
Delete event: 11
Issue comment event: 36
Push event: 88
Pull request review comment event: 7
Pull request review event: 11
Pull request event: 31
Fork event: 8

Committers

Last synced: almost 3 years ago

All Time

Total Commits: 1,441
Total Committers: 15
Avg Commits per committer: 96.067
Development Distribution Score (DDS): 0.09

Top Committers

Name	Email	Commits
Stéphane Caron	s**n@n**g	1,311
Stéphane Caron	s**n@l**r	101
Nikitas Rontsis	n**s@g**m	8
Dustin Kenefake	D**e@t**u	5
=	j**e@m**m	3
suraj2596	s**6@g**m	2
Donato Meoli	d**5@g**m	2
Pavel Otta	o**v@g**m	2
Justin Carpentier	j**r@i**r	1
Giacomo Mazzamuto	g**o@c**t	1
Soeren Wolfers	s**s@g**m	1
Takuma Ishikawa	n**u@u**m	1
Nicola Vitucci	n**i@g**m	1
rachel madden	r**n@g**m	1
Brian Delhaisse	b**e@g**m	1

Committer Domains (Top 20 + Academic)

cnr.it: 1 inria.fr: 1 microsoft.com: 1 tamu.edu: 1 lirmm.fr: 1 normalesup.org: 1

Issues and Pull Requests

Last synced: 4 months ago

All Time

Total issues: 57
Total pull requests: 145
Average time to close issues: about 2 months
Average time to close pull requests: 8 days
Total issue authors: 23
Total pull request authors: 21
Average comments per issue: 1.54
Average comments per pull request: 1.03
Merged pull requests: 131
Bot issues: 0
Bot pull requests: 0

Past Year

Issues: 6
Pull requests: 35
Average time to close issues: 13 days
Average time to close pull requests: 3 days
Issue authors: 5
Pull request authors: 7
Average comments per issue: 0.83
Average comments per pull request: 1.11
Merged pull requests: 29
Bot issues: 0
Bot pull requests: 0

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microprediction (4)
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rxian (1)
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DManowitz (1)
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Pull Request Authors

stephane-caron (131)
ottapav (3)
RSchwan (2)
dmeoli (2)
lvjonok (2)
shaoanlu (2)
joaospinto (2)
sanurielf (2)
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adamheins (1)
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Issue Labels

enhancement (12) bug (11) new solver (5) help welcome (2) good first issue (2) dependencies (1) support (1) solver watch (1)

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Packages

Total packages: 2
Total downloads:
- pypi 151,585 last-month
Total docker downloads: 56

Total dependent packages: 28
(may contain duplicates)
Total dependent repositories: 163
(may contain duplicates)
Total versions: 67
Total maintainers: 3

pypi.org: qpsolvers

Quadratic programming solvers in Python with a unified API.

Homepage: https://github.com/qpsolvers/qpsolvers
Documentation: https://qpsolvers.github.io/qpsolvers/
License: GNU Lesser General Public License v3 (LGPLv3)
Latest release: 4.8.1
published 5 months ago

Versions: 65
Dependent Packages: 27
Dependent Repositories: 163
Downloads: 151,585 Last month
Docker Downloads: 56

Rankings

Dependent packages count: 0.5%

Dependent repos count: 1.2%

Downloads: 2.3%

Average: 2.6%

Stargazers count: 3.1%

Docker downloads count: 3.5%

Forks count: 5.0%

Maintainers (1)

stephane-caron

Last synced: 4 months ago

spack.io: py-qpsolvers

Unified interface to convex Quadratic Programming (QP) solvers available in Python.

Homepage: https://github.com/qpsolvers/qpsolvers
License: []
Latest release: 3.2.0
published over 2 years ago

Versions: 2
Dependent Packages: 1
Dependent Repositories: 0

Rankings

Dependent repos count: 0.0%

Stargazers count: 11.9%

Forks count: 13.4%

Average: 20.6%

Dependent packages count: 57.3%

Maintainers (2)

adamjstewart meyersbs

Last synced: 4 months ago

Dependencies

.github/workflows/test.yml actions

actions/checkout v3 composite
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pyproject.toml pypi

numpy >= 1.15.4
scipy >=1.2.0

.github/workflows/docs.yml actions

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tarides/changelog-check-action v2 composite

doc/environment.yml conda

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qpsolvers

qpsolvers

Science Score: 54.0%

Keywords

Repository

Basic Info

Statistics

Topics

Metadata Files

README.md

Quadratic Programming Solvers in Python

Example

Installation

From conda-forge

From PyPI

Solvers

Frequently Asked Questions

Benchmark

Citing qpsolvers

Contributing

See also

Owner

Citation (CITATION.cff)

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Dependencies