A numerical illustration of a recently proposed strongly polynomial-time algorithm for the general linear programming problem

TL;DR

This paper provides a numerical example demonstrating a recently developed strongly polynomial-time algorithm for solving general linear programming problems, illustrating its efficiency and operation.

Contribution

It offers a numerical illustration of a new strongly polynomial-time LP algorithm, including examples and iteration bounds to aid understanding.

Findings

Algorithm stops in at most 2(k+n) iterations

Provides solutions or indicates infeasibility

Illustrates the algorithm with Klee-Minty and Beale LP problems

Abstract

This article presents a numerical illustration of a recently proposed strongly polynomial-time algorithm for the general linear programming (LP) problem. Each iteration of the proposed algorithm consists of two Gauss-Jordan pivoting operations. In this article, illustrative example LP problem instances include a Klee-Minty LP problem and an LP problem of Beale. The algorithm stops in at most 2(k+n) iterations, with a solution of (Eq) or, else, with an indication that (Eq) has no solutions, where k is the number of constraints of the LP problem instance stated in Neumann symmetric form, and n is the number of variables. One of the objectives of this numerical illustration article is to facilitate an understanding of how the recently proposed algorithm works.