A Simpler Approach to Linear Programming

2019/07/17 by Jean-Louis Lassez, Lassez, Jean-Louis
Computer Science · Mathematics · #90c05 #Advanced Differential Equations and Dynamical Systems #Advanced Optimization Algorithms Research #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Optimization and Control (math.OC) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1907.07811

openalex publication_date 2019/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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