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            "Development Status :: 5 - Production/Stable",
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            "License :: OSI Approved :: GNU Lesser General Public License v3 (LGPLv3)",
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            "Programming Language :: Python :: 3",
            "Programming Language :: Python :: 3.7",
            "Programming Language :: Python :: 3.8",
            "Programming Language :: Python :: 3.9",
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            "Topic :: Scientific/Engineering :: Mathematics"
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        "description": "# QP Solvers for Python\n\n[**Installation**](https://github.com/stephane-caron/qpsolvers#installation)\n| [**Documentation**](https://scaron.info/doc/qpsolvers/)\n| [**Example**](https://github.com/stephane-caron/qpsolvers#example)\n| [**Solvers**](https://github.com/stephane-caron/qpsolvers#solvers)\n| [**FAQ**](https://github.com/stephane-caron/qpsolvers#frequently-asked-questions)\n| [**Benchmark**](https://github.com/stephane-caron/qpsolvers#benchmark)\n\n[![Build](https://img.shields.io/github/workflow/status/stephane-caron/qpsolvers/CI)](https://github.com/stephane-caron/qpsolvers/actions)\n[![Coverage](https://coveralls.io/repos/github/stephane-caron/qpsolvers/badge.svg?branch=master)](https://coveralls.io/github/stephane-caron/qpsolvers?branch=master)\n[![PyPI version](https://img.shields.io/pypi/v/qpsolvers)](https://pypi.org/project/qpsolvers/)\n![Status](https://img.shields.io/pypi/status/qpsolvers)\n\nUnified interface to Quadratic Programming (QP) solvers available in Python.\n\n## Installation\n\n```sh\npip install qpsolvers\n```\nCheck out the documentation for [Python 2](https://scaron.info/doc/qpsolvers/installation.html#python-2) or [Windows](https://scaron.info/doc/qpsolvers/installation.html#windows) instructions.\n\n## Usage\n\nThe library provides a one-stop shop ``solve_qp(P, q, G, h, A, b, lb, ub)`` function with a ``solver`` keyword argument to select the backend solver. It solves convex quadratic programs in standard form:\n\n> ![Quadratic program in standard form](https://raw.githubusercontent.com/stephane-caron/qpsolvers/master/doc/src/images/qp.gif)\n\nVector inequalities are taken coordinate by coordinate. For most solvers, the matrix *P* should be [positive definite](https://en.wikipedia.org/wiki/Definite_symmetric_matrix).\n\n## Example\n\nTo solve a quadratic program, build the matrices that define it and call the ``solve_qp`` function:\n\n```python\nfrom numpy import array, dot\nfrom qpsolvers import solve_qp\n\nM = array([[1., 2., 0.], [-8., 3., 2.], [0., 1., 1.]])\nP = dot(M.T, M)  # this is a positive definite matrix\nq = dot(array([3., 2., 3.]), M)\nG = array([[1., 2., 1.], [2., 0., 1.], [-1., 2., -1.]])\nh = array([3., 2., -2.])\nA = array([1., 1., 1.])\nb = array([1.])\n\nx = solve_qp(P, q, G, h, A, b)\nprint(\"QP solution: x = {}\".format(x))\n```\n\nThis example outputs the solution ``[0.30769231, -0.69230769,  1.38461538]``.\n\n## Solvers\n\nThe list of supported solvers currently includes:\n\n| Solver | Keyword | Type | License | Warm-start |\n| ------ | ------- | ---- | ------- |------------|\n| [CVXOPT](http://cvxopt.org/) | ``cvxopt`` | Dense | GPL-3.0 | \u2714\ufe0f |\n| [ECOS](https://web.stanford.edu/~boyd/papers/ecos.html) | ``ecos`` | Sparse | GPL-3.0 | \u2716\ufe0f |\n| [Gurobi](https://www.gurobi.com/) | ``gurobi`` | Sparse | Commercial | \u2716\ufe0f |\n| [MOSEK](https://mosek.com/) | ``mosek`` | Sparse | Commercial | \u2714\ufe0f |\n| [OSQP](https://github.com/oxfordcontrol/osqp) | ``osqp`` | Sparse | Apache-2.0 | \u2714\ufe0f |\n| [qpOASES](https://github.com/coin-or/qpOASES) | ``qpoases`` | Dense | LGPL-2.1 | \u2796 |\n| [qpSWIFT](https://github.com/qpSWIFT/qpSWIFT) | ``qpswift`` | Sparse | GPL-3.0 | \u2716\ufe0f |\n| [quadprog](https://pypi.python.org/pypi/quadprog/) | ``quadprog`` | Dense | GPL-2.0 | \u2716\ufe0f |\n| [SCS](https://github.com/cvxgrp/scs) | ``scs`` | Sparse | MIT | \u2714\ufe0f |\n\n## Frequently Asked Questions\n\n- *Can I print the list of solvers available on my machine?*\n  - Absolutely: ``print(qpsolvers.available_solvers)``\n- *Is it possible to solve a least squares rather than a quadratic program?*\n  - Yes, `qpsolvers` also provides a [solve\\_ls](https://scaron.info/doc/qpsolvers/least-squares.html#qpsolvers.solve_ls) function.\n- *I have a squared norm in my cost function, how can I apply a QP solver to my problem?*\n  - You can [cast squared norms to QP matrices](https://scaron.info/teaching/conversion-from-least-squares-to-quadratic-programming.html) and feed the result to `solve_qp`.\n- *I have a non-convex quadratic program. Is there a solver I can use?*\n  - Unfortunately most available QP solvers are designed for convex problems.\n  - If your cost matrix *P* is semi-definite rather than definite, try OSQP.\n  - If your problem has concave components, go for a nonlinear solver such as [IPOPT](https://pypi.org/project/ipopt/) *e.g.* using [CasADi](https://web.casadi.org/).\n- *I get the following [build error on Windows](https://github.com/stephane-caron/qpsolvers/issues/28) when running `pip install qpsolvers`.*\n  - You will need to install the [Visual C++ Build Tools](https://visualstudio.microsoft.com/visual-cpp-build-tools/) to build all package dependencies.\n\n## Benchmark\n\nOn a [dense problem](examples/benchmark_dense_problem.py), the performance of all solvers (as measured by IPython's ``%timeit`` on an Intel(R) Core(TM) i7-6700K CPU @ 4.00GHz) is:\n\n| Solver   | Type   | Time (ms) |\n| -------- | ------ | --------- |\n| qpswift  | Dense  | 0.008     |\n| quadprog | Dense  | 0.01      |\n| qpoases  | Dense  | 0.02      |\n| osqp     | Sparse | 0.03      |\n| scs      | Sparse | 0.03      |\n| ecos     | Sparse | 0.27      |\n| cvxopt   | Dense  | 0.44      |\n| gurobi   | Sparse | 1.74      |\n| cvxpy    | Sparse | 5.71      |\n| mosek    | Sparse | 7.17      |\n\nOn a [sparse problem](examples/benchmark_sparse_problem.py) with *n = 500* optimization variables, these performances become:\n\n| Solver   | Type   | Time (ms) |\n| -------- | ------ | --------- |\n| osqp     | Sparse |    1      |\n| qpswift  | Dense  |    2      |\n| scs      | Sparse |    4      |\n| cvxpy    | Sparse |   11      |\n| mosek    | Sparse |   17      |\n| ecos     | Sparse |   33      |\n| cvxopt   | Dense  |   51      |\n| gurobi   | Sparse |  221      |\n| quadprog | Dense  |  427      |\n| qpoases  | Dense  | 1560      |\n\nOn a [model predictive control](examples/model_predictive_control.py) problem for robot locomotion, we get:\n\n| Solver   | Type   | Time (ms) |\n| -------- | ------ | --------- |\n| quadprog | Dense  | 0.03      |\n| qpswift  | Dense  | 0.08      |\n| qpoases  | Dense  | 0.36      |\n| osqp     | Sparse | 0.48      |\n| ecos     | Sparse | 0.69      |\n| scs      | Sparse | 0.76      |\n| cvxopt   | Dense  | 2.75      |\n| cvxpy    | Sparse | 7.02      |\n\nFinally, here is a small benchmark of [random dense problems](examples/benchmark_random_problems.py) (each data point corresponds to an average over 10 runs):\n\n<img src=\"https://scaron.info/images/qp-benchmark-2022.png\">\n\nNote that performances of QP solvers largely depend on the problem solved. 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