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Quadratic Programming solvers for Python with a unified API

Project description

This module provides a single function solve_qp(P, q, G, h, A, b, lb, ub, solver=X) with a solver keyword argument to select the backend solver. The quadratic program it solves is, in standard form:

https://latex.codecogs.com/gif.latex?%5Cbegin%7Bequation%7D%20%5Cbegin%7Baligned%7D%20%7B%5Ccolor%7BBlack%7D%20%5Cunderset%7Bx%7D%7B%5Ctextrm%7Bminimize%7D%7D%20%5Cquad%7D%20%26%20%7B%5Ccolor%7BBlack%7D%20%5Cfrac%7B1%7D%7B2%7D%20x%5ET%20P%20x%20+%20q%5ET%20x%7D%20%5C%5C%20%7B%5Ccolor%7BBlack%7D%20%5Ctextrm%7Bsubject%20to%7D%20%5Cquad%7D%20%26%20%7B%5Ccolor%7BBlack%7D%20Gx%20%5Cleq%20h%7D%20%5C%5C%20%26%20%7B%5Ccolor%7BBlack%7D%20Ax%20%3D%20b%7D%20%5C%5C%20%26%20%7B%5Ccolor%7BBlack%7D%20%5Cmathit%7Blb%7D%20%5Cleq%20x%20%5Cleq%20%5Cmathit%7Bub%7D%7D%20%5Cend%7Baligned%7D%20%5Cend%7Bequation%7D

where vector inequalities are taken coordinate by coordinate.

Solvers

The list of supported solvers currently includes:

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].

Project details


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