linprog

This directory contains a suite of files for performing the standard two phase simplex method on linear programming problems. The three files LINPROG.DOC, PHASEI.DOC and PHASEII.DOC are fully documented versions of the m-files LINPROG.M, PHASEI.M and PHASEII.DOC are fully documented versions of the m-files LINPROG.M, PHASEI.M and PHASEII.M. In addition, there are a number of mat-files containing examples.

The files OPT1.MAT, OPT2.MAT and OPT3.MAT contain matrices for LP's possessing an optimal solution. These particular LP's are of a type attributed to V. Klee for which the m x 2m system of constraints requires 2^m - 1 iterations (half during phase I and half during phase II). The file INFEAS.MAT contains an LP that is infeasible. The file PHIDEGEN.MAT contains an LP for which phase I produces a degenerate solution, but for which the original LP has an optimal solution. The file UNBOUND.MAT contains an LP that has an unbounded, feasible ray along which the objective value will tend to infinity.

These files should perform well on 'small' problems where A is m x n with m,n < 100 . This version does NOT implement the Revised Simplex Method and it uses neither any implicit inverse update schemes nor any sophisticated entering variable selection scheme.