_solve_simplex(T, n, basis, callback, postsolve_args, maxiter=1000, tol=1e-09, phase=2, bland=False, nit0=0)
Minimize:
c @ x
Subject to:
A @ x == b
x >= 0
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
.
The number of true variables in the problem.
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
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
x
fun
fun
success
success
slack
slack
con
con
phase
phase
status
status
nit
nit
message
message
Data needed by _postsolve to convert the solution to the standard-form problem into the solution to the original problem.
The maximum number of iterations to perform before aborting the optimization.
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.
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.
If True, choose pivots using Bland's rule . 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.
The initial iteration number used to keep an accurate iteration total in a two-phase problem.
The number of iterations. Used to keep an accurate iteration total in the two-phase problem.
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
Solve a linear programming problem in "standard form" using the Simplex Method. Linear Programming is intended to solve the following problem form:
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