Linear programming

To solve a linear program, simply build the matrices that define it and call the solve_lp() function:

from numpy import array
from lpsolvers import solve_lp

c = array([1., 2., 3.])
G = array([[1., 2., -1.], [2., 0., 1.], [1., 2., 1.], [-1., -1., -1.]])
h = array([4., 1., 3., 2.])

x = solve_lp(c, G, h)
print(f"LP solution: x = {x}")

This example outputs the solution [0.30769231, -0.69230769,  1.38461538]. The solve_qp() function accepts a solver keyword argument to select the backend solver:

lpsolvers.solve_lp(c, G, h, A=None, b=None, solver=None, **kwargs)

Solve a linear program using one of the available LP solvers.

The linear program is defined as:

\[\begin{split}\begin{split}\begin{array}{ll} \mbox{minimize} & c^T x \\ \mbox{subject to} & G x \leq h \\ & A x = b \end{array}\end{split}\end{split}\]
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]) – Name of the LP solver to choose in lpsolvers.available_solvers.

Return type:

ndarray

Returns:

Optimal solution if found, None otherwise.

Raises:

  • ValueError – If the LP is not feasible.

  • SolverNotFound – If the requested LP solver is not found.

Notes

Extra keyword arguments given to this function are forwarded to the underlying solver. For example, we can call ProxQP with a custom absolute feasibility tolerance by solve_lp(c, G, h, solver='proxqp', eps_abs=1e-8).

Installed solvers are listed in:

lpsolvers.available_solvers = ['cdd', 'cvxopt', 'cvxpy', 'pdlp', 'proxqp']

Built-in mutable sequence.

If no argument is given, the constructor creates a new empty list. The argument must be an iterable if specified.

See the examples/ folder in the repository for other use cases. For more context you can also check out this post on linear programming in Python.