QP Solvers for Python

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

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 documentation for advanced installation instructions.

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 quadratic program it solves is, in standard form:

Vector inequalities are taken coordinate by coordinate.

The list of supported solvers currently includes:

• Dense solvers:
  • CVXOPT
  • qpOASES
  • quadprog
• Sparse solvers:
  • ECOS
  • Gurobi
  • MOSEK
  • OSQP

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.])

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].

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

On a sparse problem, these performances become:

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.