A strongly polynomial-time algorithm for the general linear programming problem
Abstract
This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined 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. The algorithm requires no more than 2(k+n) iterations, as there are only k+n complementary pairs of columns to compare one-pair-at-a-time, where k is the number of constraints and n is the number of variables of given general linear programming problem. Numerical illustration is given that includes an instance of a classical problem of Klee and Minty and a problem of Beale.
Cite
@article{arxiv.2503.12041,
title = {A strongly polynomial-time algorithm for the general linear programming problem},
author = {Samuel Awoniyi},
journal= {arXiv preprint arXiv:2503.12041},
year = {2026}
}
Comments
30 pages; Based on latest reviewers' and readers' suggestions, especially two Reviews by a reputable journal, the illustrative examples have been given additional annotation to enhance reader's understanding and possibly save reader's time. The computational complexity result is now 2(k+n) instead of k+n