Some applications of the Semi-Infinite Simplex Algorithm

Abstract

The Semi-Infinite Simplex Algorithm (SISA) with applications to so called Semi-Infinite Linear Programs (SILP) with capacity constraints as a direct analog to column generating techniques in linear programming methods of was presented by the author in 1978. Later in 1981, the SISA for SILP in partially ordered spaces was described with more algebraic framework in terms of feasible basic solutions, extreme points and so on. Now this paper has two aims: to reflect the history of one branch of the so-called Leipzig-Optimization-Tree with roots J. Focke/A. Göpfert / R. Klötzler and to demonstrate some applications of the Simplex Algorithm.

Keywords:

• semi-infinite programs
• capacity constraints
• simplex algorithm
• optimization in vector spaces

AMS Subject Classifications:

• 90C29
• 90C26
• 58C07
• 90C48