Linear programming on non-compact polytopes and the Kuratowski convergence with application in economics

TL;DR

This paper provides a geometric characterization of optimal solutions in general linear programming without compactness assumptions and studies the convergence of polyhedra and solutions using Kuratowski convergence, with applications in economics.

Contribution

It introduces a geometric approach to characterize optimal solutions in non-compact linear programming and analyzes solution behavior under polyhedral convergence.

Findings

Characterization of optimal basic solutions without compactness

Analysis of Kuratowski convergence of polyhedra

Insights into solution stability in economic models

Abstract

The aims of this article are two-fold. First, we give a geometric characterization of the optimal basic solutions of the general linear programming problem (no compactness assumptions) and provide a simple, self-contained proof of it together with an economical interpretation. Then, we turn to considering a dynamic version of the linear programming problem in that we consider the Kuratowski convergence of polyhedra and study the behaviour of optimal solutions. Our methods are purely geometric.