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

Summary · qwen2.5:32b

A recently proposed strongly polynomial-time algorithm for solving general linear programming problems has been validated, combining primal and dual problems into a system constrained by complementarity relations. The algorithm uses iterative complementary Gauss-Jordan pivoting operations guided by a necessary-condition lemma. It is proven to require no more than 2(k+n) iterations, with k being the number of constraints and n the number of variables.

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Excerpt

arXiv:2310.05855v5 Announce Type: replace 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.