Quadratic programming solvers in Python with a unified API
Project description
QP Solvers for Python
Wrapper around Quadratic Programming (QP) solvers in Python, with a unified interface.
Installation
sudo apt install python3dev 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:
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)
 Absolutely:
 Is it possible to solve a least squares rather than a quadratic program?
 Yes,
qpsolvers
also provides a solve_ls function.
 Yes,
 I have a squared norm in my cost function, how can I apply a QP solver to my problem?
 You can cast squared norms to QP matrices and feed the result to
solve_qp
.
 You can cast squared norms to QP matrices and feed the result to
 I have a nonconvex quadratic program. Is there a solver I can use?
 I get the following build error on Windows when running
pip install qpsolvers
. You will need to install the Visual C++ Build Tools to build all package dependencies.
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 SecondOrder Cone Programming (SOCP) which the documentation advises bypassing for better performance. Similarly, ECOS reformulates from QP to SOCP and works best on small problems.
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