A strongly polynomial-time algorithm for the general linear programming problem
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918400639369216 |
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| author | Awoniyi, Samuel |
| author_facet | Awoniyi, Samuel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12041 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A strongly polynomial-time algorithm for the general linear programming problem Awoniyi, Samuel Optimization and Control Math OC 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. |
| title | A strongly polynomial-time algorithm for the general linear programming problem |
| topic | Optimization and Control Math OC |
| url | https://arxiv.org/abs/2503.12041 |