# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1907.07811