scipy.optimize._linprog_simplex:_solve_simplex

Parameters

T : 2-D array

A 2-D array representing the simplex tableau, T, corresponding to the linear programming problem. It should have the form:

[[A[0, 0], A[0, 1], ..., A[0, n_total], b[0]],

[A[1, 0], A[1, 1], ..., A[1, n_total], b[1]], . . . [A[m, 0], A[m, 1], ..., A[m, n_total], b[m]], [c[0], c[1], ..., c[n_total], 0]]

for a Phase 2 problem, or the form:

[[A[0, 0], A[0, 1], ..., A[0, n_total], b[0]],

[A[1, 0], A[1, 1], ..., A[1, n_total], b[1]], . . . [A[m, 0], A[m, 1], ..., A[m, n_total], b[m]], [c[0], c[1], ..., c[n_total], 0], [c'[0], c'[1], ..., c'[n_total], 0]]

for a Phase 1 problem (a problem in which a basic feasible solution is sought prior to maximizing the actual objective. T is modified in place by _solve_simplex.

n : int

The number of true variables in the problem.

basis : 1-D array

An array of the indices of the basic variables, such that basis[i] contains the column corresponding to the basic variable for row i. Basis is modified in place by _solve_simplex

callback : callable, optional

If a callback function is provided, it will be called within each iteration of the algorithm. The callback must accept a scipy.optimize.OptimizeResult consisting of the following fields:

x

Current solution vector

fun

Current value of the objective function

success

True only when a phase has completed successfully. This will be False for most iterations.

slack

The values of the slack variables. Each slack variable corresponds to an inequality constraint. If the slack is zero, the corresponding constraint is active.

con

The (nominally zero) residuals of the equality constraints, that is, b - A_eq @ x

phase

The phase of the optimization being executed. In phase 1 a basic feasible solution is sought and the T has an additional row representing an alternate objective function.

status

An integer representing the exit status of the optimization

0 : Optimization terminated successfully
1 : Iteration limit reached
2 : Problem appears to be infeasible
3 : Problem appears to be unbounded
4 : Serious numerical difficulties encountered

nit

The number of iterations performed.

message

A string descriptor of the exit status of the optimization.

postsolve_args : tuple

Data needed by _postsolve to convert the solution to the standard-form problem into the solution to the original problem.

maxiter : int

The maximum number of iterations to perform before aborting the optimization.

tol : float

The tolerance which determines when a solution is "close enough" to zero in Phase 1 to be considered a basic feasible solution or close enough to positive to serve as an optimal solution.

phase : int

The phase of the optimization being executed. In phase 1 a basic feasible solution is sought and the T has an additional row representing an alternate objective function.

bland : bool

If True, choose pivots using Bland's rule ^[3]. In problems which fail to converge due to cycling, using Bland's rule can provide convergence at the expense of a less optimal path about the simplex.

nit0 : int

The initial iteration number used to keep an accurate iteration total in a two-phase problem.