`scipy.optimize._linprog_util:_get_Abc`

Signature

def _get_Abc(lp, c0)

Given a linear programming problem of the form:

Minimize

c @ x

Subject to

A_ub @ x <= b_ub
A_eq @ x == b_eq
 lb <= x <= ub

where lb = 0 and ub = None unless set in bounds.

Return the problem in standard form:

Minimize

c @ x

Subject to

A @ x == b
    x >= 0

by adding slack variables and making variable substitutions as necessary.

lp : A `scipy.optimize._linprog_util._LPProblem` consisting of the following fields:

c: The coefficients of the linear objective function to be minimized.
A_ub: The inequality constraint matrix. Each row of A_ub specifies the coefficients of a linear inequality constraint on x.
b_ub: The inequality constraint vector. Each element represents an upper bound on the corresponding value of A_ub @ x.
A_eq: The equality constraint matrix. Each row of A_eq specifies the coefficients of a linear equality constraint on x.
b_eq: The equality constraint vector. Each element of A_eq @ x must equal the corresponding element of b_eq.
bounds: The bounds of x, lower bounds in the 1st column, upper bounds in the 2nd column. The bounds are possibly tightened by the presolve procedure.
x0: Guess values of the decision variables, which will be refined by the optimization algorithm. This argument is currently used only by the 'revised simplex' method, and can only be used if x0 represents a basic feasible solution.

c0 : float

Constant term in objective function due to fixed (and eliminated) variables.

A : 2-D array: 2-D array such that A @ x, gives the values of the equality constraints at x.
b : 1-D array: 1-D array of values representing the RHS of each equality constraint (row) in A (for standard form problem).
c : 1-D array: Coefficients of the linear objective function to be minimized (for standard form problem).
c0 : float: Constant term in objective function due to fixed (and eliminated) variables.
x0 : 1-D array: Starting values of the independent variables, which will be refined by the optimization algorithm