Dual Dictionaries in Linear Programming

TL;DR

This paper provides a conceptual proof of the bijection between primal and dual dictionaries in linear programming, facilitating the use of the Dual Simplex Method.

Contribution

It offers a concise, conceptual proof of the bijection between primal and dual dictionaries, enhancing understanding of the Dual Simplex Method.

Findings

Confirmed the existence of a bijection between primal and dual dictionaries.

Simplified the conceptual understanding of the Dual Simplex Method.

Provided a proof that can be used to justify algorithmic steps.

Abstract

In order to use the Dual Simplex Method, one needs to prove a certain bijection between the dictionaries associated with the primal problem and those associated with its dual. We give a short conceptual proof of why this bijection exists.