A Simpler Approach to Linear Programming

TL;DR

This paper presents a novel interpretation of linear programming duality by leveraging Fourier elimination and Gaussian elimination to determine the solvability of bounded systems of linear inequalities.

Contribution

It introduces a new perspective on duality theory based on implicit equalities, simplifying the decision process for linear inequalities.

Findings

Gaussian elimination can decide solvability of bounded systems

Fourier elimination relates to implicit equalities

New interpretation simplifies linear programming duality

Abstract

Dantzig and Eaves claimed that fundamental duality theorems of linear programming were a trivial consequence of Fourier elimination. Another property of Fourier elimination is considered here, regarding the existence of implicit equalities rather than solvability. This leads to a different interpretation of duality theory which allows us to use Gaussian elimination to decide solvability of systems of linear inequalities, for bounded systems.