Skip to main content

Quadratic programming solvers in Python with a unified API

Project description

QP Solvers for Python

build PyPI package Documentation Status

Wrapper around Quadratic Programming (QP) solvers in Python, with a unified interface.

Installation

sudo apt install python3-dev
pip3 install qpsolvers

Check out the documentation for Python 2 or Windows instructions.

Usage

The function solve_qp(P, q, G, h, A, b, lb, ub) is called with the solver keyword argument to select the backend solver. The convex quadratic program it solves is, in standard form:

Equation of Quadratic Program

Vector inequalities are taken coordinate by coordinate. The matrix P should be positive definite.

Example

To solve a quadratic program, simply build the matrices that define it and call the solve_qp function:

from numpy import array, dot
from qpsolvers import solve_qp

M = array([[1., 2., 0.], [-8., 3., 2.], [0., 1., 1.]])
P = dot(M.T, M)  # this is a positive definite matrix
q = dot(array([3., 2., 3.]), M).reshape((3,))
G = array([[1., 2., 1.], [2., 0., 1.], [-1., 2., -1.]])
h = array([3., 2., -2.]).reshape((3,))
A = array([1., 1., 1.])
b = array([1.])

x = solve_qp(P, q, G, h, A, b)
print("QP solution: x = {}".format(x))

This example outputs the solution [0.30769231, -0.69230769, 1.38461538].

Solvers

The list of supported solvers currently includes:

Frequently Asked Questions

  • Can I print the list of solvers available on my machine?
    • Absolutely: print(qpsolvers.available_solvers)
  • Is it possible to solve a least squares rather than a quadratic program?
    • Yes, qpsolvers also provides a solve_ls function.
  • I have a squared norm in my cost function, how can I apply a QP solver to my problem?
  • I have a non-convex quadratic program. Is there a solver I can use?
    • Unfortunately most available QP solvers are designed for convex problems.
    • If your cost matrix P is semi-definite rather than definite, try OSQP.
    • If your problem has concave components, go for a nonlinear solver such as IPOPT e.g. using CasADi.
  • I get the following build error on Windows when running pip install qpsolvers.

Performances

On a dense problem, the performance of all solvers (as measured by IPython's %timeit on my machine) is:

Solver Type Time (ms)
quadprog Dense 0.02
qpoases Dense 0.03
osqp Sparse 0.04
ecos Sparse 0.34
cvxopt Dense 0.46
gurobi Sparse 0.84
cvxpy Sparse 3.40
mosek Sparse 7.17

On a sparse problem, these performances become:

Solver Type Time (ms)
osqp Sparse 1
mosek Sparse 17
ecos Sparse 21
cvxopt Dense 186
gurobi Sparse 221
quadprog Dense 550
cvxpy Sparse 654
qpoases Dense 2250

Finally, here are the results on a benchmark of random problems (each data point corresponds to an average over 10 runs):

Note that performances of QP solvers largely depend on the problem solved. For instance, MOSEK performs an automatic conversion to Second-Order Cone Programming (SOCP) which the documentation advises bypassing for better performance. Similarly, ECOS reformulates from QP to SOCP and works best on small problems.

Project details


Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Files for qpsolvers, version 1.6.1
Filename, size File type Python version Upload date Hashes
Filename, size qpsolvers-1.6.1-py3-none-any.whl (23.7 kB) File type Wheel Python version py3 Upload date Hashes View
Filename, size qpsolvers-1.6.1.tar.gz (29.2 kB) File type Source Python version None Upload date Hashes View

Supported by

AWS AWS Cloud computing Datadog Datadog Monitoring DigiCert DigiCert EV certificate Facebook / Instagram Facebook / Instagram PSF Sponsor Fastly Fastly CDN Google Google Object Storage and Download Analytics Microsoft Microsoft PSF Sponsor Pingdom Pingdom Monitoring Salesforce Salesforce PSF Sponsor Sentry Sentry Error logging StatusPage StatusPage Status page