Geometric fundamentals of the simplex method in semi-infinite programming

Abstract

The natural extension of the simplex method to linear optimization problems with infinitely many constraints applies to their dual problems. Although the feasible sets are convex sets in spaces of generalized finite sequences, they preserve many of the properties of polyhedral convex sets in finite dimensional spaces. These properties are fundamental in obtaining a geometrical interpretation of the pivot operation. The problem of finding a basic set is also analyzed.