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This article presents a validation of a recently proposed stronglypolynomial-time algorithm for the general linear programming problem. Thealgorithm is an implicit, solution-space reduction procedure that works asfollows. Primal and dual problems are combined into a special system of linearequations constrained by complementarity relations and non-negative variables.Each iteration of the algorithm consists of applying two complementaryGauss-Jordan pivoting operations, guided by a reduction lemma. The algorithmrequires no more than m+n iterations, where m is the number of constraints andn is the number of variables of the general linear programming problem. Inanother arXiv article, arXiv:2309.01037[math.DC], a numerical illustration ofthe algorithm is given that includes an instance of a classical problem of Kleeand Minty and a problem of Beale.

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