A numerical illustration of a recently proposed strongly polynomial-time algorithm for the general linear programming problem
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866918493103849472 |
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| author | Awoniyi, Samuel |
| author_facet | Awoniyi, Samuel |
| contents | This article presents a numerical illustration of a recently proposed strongly polynomial-time algorithm for the general linear programming (LP) problem. Each iteration of the proposed algorithm consists of two Gauss-Jordan pivoting operations. In this article, illustrative example LP problem instances include a Klee-Minty LP problem and an LP problem of Beale. The algorithm stops in at most 2(k+n) iterations, with a solution of (Eq) or, else, with an indication that (Eq) has no solutions, where k is the number of constraints of the LP problem instance stated in Neumann symmetric form, and n is the number of variables. One of the objectives of this numerical illustration article is to facilitate an understanding of how the recently proposed algorithm works. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_01037 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A numerical illustration of a recently proposed strongly polynomial-time algorithm for the general linear programming problem Awoniyi, Samuel Optimization and Control Math OC This article presents a numerical illustration of a recently proposed strongly polynomial-time algorithm for the general linear programming (LP) problem. Each iteration of the proposed algorithm consists of two Gauss-Jordan pivoting operations. In this article, illustrative example LP problem instances include a Klee-Minty LP problem and an LP problem of Beale. The algorithm stops in at most 2(k+n) iterations, with a solution of (Eq) or, else, with an indication that (Eq) has no solutions, where k is the number of constraints of the LP problem instance stated in Neumann symmetric form, and n is the number of variables. One of the objectives of this numerical illustration article is to facilitate an understanding of how the recently proposed algorithm works. |
| title | A numerical illustration of a recently proposed strongly polynomial-time algorithm for the general linear programming problem |
| topic | Optimization and Control Math OC |
| url | https://arxiv.org/abs/2309.01037 |