Quadratic programming solvers in Python with a unified API.
Project description
Quadratic Programming Solvers in Python
Unified interface to convex Quadratic Programming (QP) solvers available in Python.
Installation
Using PyPI
pip install qpsolvers
Using
conda install qpsolvers c condaforge
Check out the documentation for Windows instructions.
Usage
The library provides a onestop shop solve_qp
function with a solver
keyword argument to select the backend solver. It solves convex quadratic programs in standard form:
$$ \begin{split} \begin{array}{ll} \underset{x}{\mbox{minimize}} & \frac{1}{2} x^T P x + q^T x \ \mbox{subject to} & G x \leq h \ & A x = b \ & lb \leq x \leq ub \end{array} \end{split} $$
Vector inequalities apply coordinate by coordinate. The function returns the solution $x^*$ found by the solver, or None
in case of failure/unfeasible problem. All solvers require the problem to be convex, meaning the matrix $P$ should be positive semidefinite. Some solvers further require the problem to be strictly convex, meaning $P$ should be positive definite.
Dual multipliers: alternatively, the solve_problem
function returns a more complete solution object containing both the primal solution and its corresponding dual multipliers.
Example
To solve a quadratic program, build the matrices that define it and call the solve_qp
function:
import numpy as np
from qpsolvers import solve_qp
M = np.array([[1.0, 2.0, 0.0], [8.0, 3.0, 2.0], [0.0, 1.0, 1.0]])
P = M.T @ M # this is a positive definite matrix
q = np.array([3.0, 2.0, 3.0]) @ M
G = np.array([[1.0, 2.0, 1.0], [2.0, 0.0, 1.0], [1.0, 2.0, 1.0]])
h = np.array([3.0, 2.0, 2.0])
A = np.array([1.0, 1.0, 1.0])
b = np.array([1.0])
x = solve_qp(P, q, G, h, A, b, solver="proxqp")
print(f"QP solution: x = {x}")
This example outputs the solution [0.30769231, 0.69230769, 1.38461538]
. It is also possible to get dual multipliers at the solution, as shown in this example.
Solvers
Solver  Keyword  Algorithm  API  License  Warmstart 

Clarabel  clarabel 
Interior point  Sparse  Apache2.0  ✖️ 
CVXOPT  cvxopt 
Interior point  Dense  GPL3.0  ✔️ 
DAQP  daqp 
Active set  Dense  MIT  ✖️ 
ECOS  ecos 
Interior point  Sparse  GPL3.0  ✖️ 
Gurobi  gurobi 
Interior point  Sparse  Commercial  ✖️ 
HiGHS  highs 
Active set  Sparse  MIT  ✖️ 
MOSEK  mosek 
Interior point  Sparse  Commercial  ✔️ 
NPPro  nppro 
Active set  Dense  Commercial  ✔️ 
OSQP  osqp 
Augmented Lagrangian  Sparse  Apache2.0  ✔️ 
ProxQP  proxqp 
Augmented Lagrangian  Dense & Sparse  BSD2Clause  ✔️ 
qpOASES  qpoases 
Active set  Dense  LGPL2.1  ➖ 
qpSWIFT  qpswift 
Interior point  Sparse  GPL3.0  ✖️ 
quadprog  quadprog 
Active set  Dense  GPL2.0  ✖️ 
SCS  scs 
Augmented Lagrangian  Sparse  MIT  ✔️ 
Matrix arguments are NumPy arrays for dense solvers and SciPy Compressed Sparse Column (CSC) matrices for sparse ones.
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, there is also a
solve_ls
function.
 Yes, there is also a
 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?
 Unfortunately most available QP solvers are designed for convex problems (i.e. problems for which
P
is positive semidefinite). That's in a way expected, as solving nonconvex QP problems is NP hard.  CPLEX has methods for solving nonconvex quadratic problems to either local or global optimality. Notice that finding global solutions can be significantly slower than finding local solutions.
 Gurobi can find global solutions to nonconvex quadratic problems.
 For a free nonconvex solver, you can try the popular nonlinear solver IPOPT e.g. using CasADi.
 A list of (convex/nonconvex) quadratic programming software (not necessarily in Python) was compiled by Nick Gould and Phillip Toint.
 Unfortunately most available QP solvers are designed for convex problems (i.e. problems for which
 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.
 Can I help?
 Absolutely! The first step is to install the library and use it. Report any bug in the issue tracker.
 If you're a developer looking to hack on open source, check out the contribution guidelines for suggestions.
Benchmark
On a dense problem, the performance of all solvers (as measured by IPython's %timeit
on an Intel(R) Core(TM) i76700K CPU @ 4.00GHz) is:
Solver  Type  Time (ms) 

qpswift  Dense  0.008 
quadprog  Dense  0.01 
qpoases  Dense  0.02 
osqp  Sparse  0.03 
scs  Sparse  0.03 
ecos  Sparse  0.27 
cvxopt  Dense  0.44 
gurobi  Sparse  1.74 
mosek  Sparse  7.17 
On a sparse problem with n = 500 optimization variables, these performances become:
Solver  Type  Time (ms) 

osqp  Sparse  1 
qpswift  Dense  2 
scs  Sparse  4 
mosek  Sparse  17 
ecos  Sparse  33 
cvxopt  Dense  51 
gurobi  Sparse  221 
quadprog  Dense  427 
qpoases  Dense  1560 
On a model predictive control problem for robot locomotion, we get:
Solver  Type  Time (ms) 

quadprog  Dense  0.03 
qpswift  Dense  0.08 
qpoases  Dense  0.36 
osqp  Sparse  0.48 
ecos  Sparse  0.69 
scs  Sparse  0.76 
cvxopt  Dense  2.75 
Finally, here is a small benchmark of random dense 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.
Contributing
We welcome contributions, see Contributing for details.
We are also looking forward to hearing about your use cases! Please share them in Show and tell.
Citing qpsolvers
If you find this project useful, please consider giving it a :star: and a citation :books: (check out the Cite this repository
button on GitHub).
Project details
Release history Release notifications  RSS feed
Download files
Download the file for your platform. If you're not sure which to choose, learn more about installing packages.
Source Distribution
Built Distribution
Hashes for qpsolvers3.4.0py3noneany.whl
Algorithm  Hash digest  

SHA256  2788f1cba7b64bdf7cc32fe616946784962f187bd285229ffb6b7a15b8863f28 

MD5  a2630f22028c1d9e93e2aec7ba8b3a5f 

BLAKE2b256  4cbdc0c34384e04e7fd2b437d3552dbd5d2365bbc109b1c060f8cb97b176478e 