Affine scaling with degenerate linear programming problems

Abstract

Consider the problem of maximising a linear objective function over the polyhedron,

We shall assume that℘ has a non-empty (relative) interior, and that the matrix A j has rank n thereby guaranteeing that ℘ has vertices. We describe an algorithm that generalises to the affine scaling algorithm for standard form problems, and show that, subject to a rather mild conditions, each limit point of the sequence generatsed by the algorithm is optimal, whether or not the problem is degenerate.

Keywords:

• Primal interior point
• Affine scaling
• Degenerate problems