Validation of a strongly polynomial-time algorithm for the general linear programming problem (2310.05855v2)

Abstract: This article presents a validation of a recently proposed strongly polynomial-time algorithm for the general linear programming problem. The algorithm is an implicit, solution-space 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 two complementary Gauss-Jordan pivoting operations, guided by a reduction lemma. The algorithm requires no more than m+n iterations, where m is the number of constraints and n is the number of variables of the general linear programming problem. In another arXiv article, arXiv:2309.01037[math.DC], a numerical illustration of the algorithm is given that includes an instance of a classical problem of Klee and Minty and a problem of Beale.