Supported solvers

CVXOPT

Solver interface for CVXOPT.

lpsolvers.cvxopt_.cvxopt_matrix(M)

Convert matrix M to CVXOPT format.

Parameters:: M (ndarray) – Matrix to convert.
Return type:: matrix
Returns:: Same matrix in CVXOPT format.

lpsolvers.cvxopt_.cvxopt_solve_lp(c, G, h, A=None, b=None, solver='glpk', **kwargs)

Solve a linear program using CVXOPT.

The linear program is defined by:

\[\begin{split}\begin{split}\begin{array}{ll} \mbox{minimize} & c^T x \\ \mbox{subject to} & G x \leq h \\ & A x = b \end{array}\end{split}\end{split}\]

It is solved using the LP solver from CVXOPT.

Parameters:

c (ndarray) – Linear cost vector.
G (ndarray) – Linear inequality constraint matrix.
h (ndarray) – Linear inequality constraint vector.
A (Optional[ndarray]) – Linear equality constraint matrix.
b (Optional[ndarray]) – Linear equality constraint vector.
solver (Optional[str]) – Solver to use, default is GLPK if available

Return type:

ndarray

Returns:

Optimal (primal) solution of the linear program, if it exists.

Raises:

ValueError – If the LP is not feasible.

CVXPY

Solver interface for CVXPY.

lpsolvers.cvxpy_.cvxpy_solve_lp(c, G, h, A=None, b=None, solver=None, verbose=False, **kwargs)

Solve a linear program using CVXPY.

The linear program is defined by:

\[\begin{split}\begin{split}\begin{array}{ll} \mbox{minimize} & c^T x \\ \mbox{subject to} & G x \leq h \\ & A x = b \end{array}\end{split}\end{split}\]

It is solved using a solver wrapped by CVXPY. The underlying solver is selected via the corresponding keyword argument.

Parameters:

c (ndarray) – Linear cost vector.
G (ndarray) – Linear inequality constraint matrix.
h (ndarray) – Linear inequality constraint vector.
A (Optional[ndarray]) – Linear equality constraint matrix.
b (Optional[ndarray]) – Linear equality constraint vector.
solver (Optional[str]) – Solver name in cvxpy.installed_solvers().
verbose (bool) – Set to True to print out extra information.

Returns:

x – Optimal (primal) solution of the linear program, if it exists.

Return type:

array, shape=(n,)

Raises:

ValueError – If the LP is not feasible.

cdd

Solver interface for cdd.

lpsolvers.cdd_.cdd_solve_lp(c, G, h, A=None, b=None)

Solve a linear program using the LP solver from cdd.

The linear program is defined by:

\[\begin{split}\\begin{split}\\begin{array}{ll} \\mbox{minimize} & c^T x \\\\ \\mbox{subject to} & G x \\leq h \\\\ & A x = b \\end{array}\\end{split}\end{split}\]

It is solved using cdd.

Parameters:

c (ndarray) – Linear cost vector.
G (ndarray) – Linear inequality constraint matrix.
h (ndarray) – Linear inequality constraint vector.
A (Optional[ndarray]) – Linear equality constraint matrix.
b (Optional[ndarray]) – Linear equality constraint vector.
solver – Solver to use, default is GLPK if available

Return type:

ndarray

Returns:

Optimal (primal) solution of the linear program, if it exists.

Raises:

ValueError – If the linear program is not feasible.

PDLP

Solver interface for PDLP.

PDLP is a first-order method for convex quadratic programming aiming for high-accuracy solutions and scaling to large problems. If you use PDLP in your academic works, consider citing the corresponding paper [Applegate2021].

lpsolvers.pdlp_.pdlp_solve_lp(c, G, h, A=None, b=None, verbose=False, eps_optimal_absolute=None, eps_optimal_relative=None, time_sec_limits=None, **kwargs)

Solve a quadratic program using PDLP.

Parameters:

c (ndarray) – Linear cost vector.
G (ndarray) – Linear inequality constraint matrix.
h (ndarray) – Linear inequality constraint vector.
A (Optional[ndarray]) – Linear equality constraint matrix.
b (Optional[ndarray]) – Linear equality constraint vector.
verbose (bool) – Set to True to print out extra information.
verbose – Set to True to print out extra information.
eps_optimal_absolute (Optional[float]) – Absolute tolerance on the primal-dual residuals and duality gap. See e.g. [tolerances] for an overview of solver tolerances.
eps_optimal_relative (Optional[float]) – Relative tolerance on the primal-dual residuals and duality gap. See e.g. [tolerances] for an overview of solver tolerances.
time_sec_limits (Optional[float]) – Maximum computation time the solver is allowed, in seconds.

Return type:

ndarray

Returns:

Primal solution to the QP, if found, otherwise None.

Notes

All other keyword arguments are forwarded as parameters to PDLP. For instance, you can call pdlp_solve_qp(P, q, G, h, num_threads=3, verbosity_level=2). For a quick overview, the solver accepts the following settings:

Name	Effect
`num_threads`	Number of threads to use (positive).
`verbosity_level`	Verbosity level from 0 (no logging) to 4 (extensive logging).
`initial_primal_weight`	Initial value of the primal weight (ratio of primal over dual step sizes).
`l_inf_ruiz_iterations`	Number of L-infinity Ruiz rescaling iterations applied to the constraint matrix.
`l2_norm_rescaling`	If set to `True`, applies L2-norm rescaling after Ruiz rescaling.

This list is not exhaustive. Check out the solver’s Protocol Bufffers file for more. See also the Mathematical background for PDLP.

ProxQP

Solver interface for ProxQP.

ProxQP is the QP solver from ProxSuite, a collection of open-source solvers rooted in revisited primal-dual proximal algorithms. If you use ProxQP in some academic work, consider citing the corresponding paper [Bambade2022].

lpsolvers.proxqp_.proxqp_solve_lp(c, G, h, A=None, b=None, verbose=False, backend=None, **kwargs)

Solve a quadratic program using ProxQP.

Parameters:

c (ndarray) – Linear cost vector.
G (ndarray) – Linear inequality constraint matrix.
h (ndarray) – Linear inequality constraint vector.
A (Optional[ndarray]) – Linear equality constraint matrix.
b (Optional[ndarray]) – Linear equality constraint vector.
backend (Optional[str]) – ProxQP backend to use in [None, "dense", "sparse"]. If None (default), the backend is selected based on the type of P.
verbose (bool) – Set to True to print out extra information.

Return type:

ndarray

Returns:

Solution to the QP returned by the solver.

Notes

All other keyword arguments are forwarded as solver settings to ProxQP. For instance, you can call proxqp_solve_qp(P, q, G, h, eps_abs=1e-6). Check out the solver documentation for details.