Validation of a recently proposed strongly polynomial-time algorithm for the general linear programming problem

TL;DR

This paper validates a new strongly polynomial-time algorithm for solving general linear programming problems, demonstrating it requires at most 2(k+n) iterations based on problem size.

Contribution

It provides a proof that the proposed algorithm converges within a bounded number of iterations, confirming its efficiency for linear programming.

Findings

Algorithm requires no more than 2(k+n) iterations.

Validation confirms the algorithm's strongly polynomial-time complexity.

Combines primal and dual problems using Gauss-Jordan pivoting.

Abstract

This article presents a validation of a recently proposed strongly polynomial-time algorithm for the general linear programming problem. The proposed algorithm is an implicit reduction procedure that combines primal and dual linear programming problems into a special system of linear equations constrained by complementarity relations and non-negative variables. Each iteration of the algorithm consists of applying a pair of complementary Gauss-Jordan pivoting operations, guided by a necessary-condition lemma. This validation article demonstrates that the proposed algorithm requires no more than 2(k+n) iterations, where k is the number of constraints and n is the number of variables of given general linear programming problem.