QP Solvers for Python

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

Installation

The simplest way to install this module is:

pip install qpsolvers

You can add the --user parameter for a user-only installation. See also the wiki page for advanced installation instructions.

Usage

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

Vector inequalities are taken coordinate by coordinate.

Solvers

The list of supported solvers currently includes:

Dense solvers:
- CVXOPT
- qpOASES
- quadprog
Sparse solvers:
- ECOS as wrapped by CVXPY
- Gurobi
- MOSEK
- OSQP

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)  # quick way to build a symmetric 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.])

print "QP solution:", solve_qp(P, q, G, h, A, b)

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

Performances

On the dense example above, 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
cvxopt	Dense	0.43
gurobi	Sparse	0.84
ecos	Sparse	2.61
mosek	Sparse	7.17

Meanwhile, on the sparse.py example, these performances become:

Solver	Type	Time (ms)
osqp	Sparse	1
mosek	Sparse	17
cvxopt	Dense	35
gurobi	Sparse	221
quadprog	Dense	421
ecos	Sparse	638
qpoases	Dense	2210

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