Dual Dictionaries in Linear Programming
Patrick T. Perkins, Xiang Gao

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.
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Taxonomy
TopicsAdvanced Optimization Algorithms Research · Mathematics and Applications · Polynomial and algebraic computation
