Regional division and reduction algorithm for minimizing the sum of linear fractional functions
Abstract This paper presents a practicable regional division and cut algorithm for minimizing the sum of linear fractional functions over a polyhedron. In the algorithm, by using an equivalent problem (P) of the original problem, the proposed division operation generalizes the usual standard bisecti...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-03-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-018-1651-9 |
| _version_ | 1818354601537044480 |
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| author | Pei-Ping Shen Ting Lu |
| author_facet | Pei-Ping Shen Ting Lu |
| author_sort | Pei-Ping Shen |
| collection | DOAJ |
| description | Abstract This paper presents a practicable regional division and cut algorithm for minimizing the sum of linear fractional functions over a polyhedron. In the algorithm, by using an equivalent problem (P) of the original problem, the proposed division operation generalizes the usual standard bisection, and the deleting and reduction operations can cut away a large part of the current investigated region in which the global optimal solution of (P) does not exist. The main computation involves solving a sequence of univariate equations with strict monotonicity. The proposed algorithm is convergent to the global minimum through the successive refinement of the solutions of a series of univariate equations. Numerical results are given to show the feasibility and effectiveness of the proposed algorithm. |
| first_indexed | 2024-12-13T19:28:01Z |
| format | Article |
| id | doaj.art-df8b9f4f563b4988943de03cb4da0b04 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-13T19:28:01Z |
| publishDate | 2018-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-df8b9f4f563b4988943de03cb4da0b042022-12-21T23:33:59ZengSpringerOpenJournal of Inequalities and Applications1029-242X2018-03-012018111910.1186/s13660-018-1651-9Regional division and reduction algorithm for minimizing the sum of linear fractional functionsPei-Ping Shen0Ting Lu1College of Mathematics and Information Science, Henan Normal UniversityCollege of Mathematics and Information Science, Henan Normal UniversityAbstract This paper presents a practicable regional division and cut algorithm for minimizing the sum of linear fractional functions over a polyhedron. In the algorithm, by using an equivalent problem (P) of the original problem, the proposed division operation generalizes the usual standard bisection, and the deleting and reduction operations can cut away a large part of the current investigated region in which the global optimal solution of (P) does not exist. The main computation involves solving a sequence of univariate equations with strict monotonicity. The proposed algorithm is convergent to the global minimum through the successive refinement of the solutions of a series of univariate equations. Numerical results are given to show the feasibility and effectiveness of the proposed algorithm.http://link.springer.com/article/10.1186/s13660-018-1651-9Global optimizationSum of linear ratiosRegional division and reductionFractional programming |
| spellingShingle | Pei-Ping Shen Ting Lu Regional division and reduction algorithm for minimizing the sum of linear fractional functions Journal of Inequalities and Applications Global optimization Sum of linear ratios Regional division and reduction Fractional programming |
| title | Regional division and reduction algorithm for minimizing the sum of linear fractional functions |
| title_full | Regional division and reduction algorithm for minimizing the sum of linear fractional functions |
| title_fullStr | Regional division and reduction algorithm for minimizing the sum of linear fractional functions |
| title_full_unstemmed | Regional division and reduction algorithm for minimizing the sum of linear fractional functions |
| title_short | Regional division and reduction algorithm for minimizing the sum of linear fractional functions |
| title_sort | regional division and reduction algorithm for minimizing the sum of linear fractional functions |
| topic | Global optimization Sum of linear ratios Regional division and reduction Fractional programming |
| url | http://link.springer.com/article/10.1186/s13660-018-1651-9 |
| work_keys_str_mv | AT peipingshen regionaldivisionandreductionalgorithmforminimizingthesumoflinearfractionalfunctions AT tinglu regionaldivisionandreductionalgorithmforminimizingthesumoflinearfractionalfunctions |