A novel algorithm for solving sum of several affine fractional functions
By using the outer space branch-and-reduction scheme, we present a novel algorithm for globally optimizing the sum of several affine fractional functions problem (SAFFP) over a nonempty compact set. For providing the reliable lower bounds in the searching process of iterations, we devise a novel lin...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-02-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023464?viewType=HTML |
| _version_ | 1811160947553730560 |
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| author | Hongwu Li Yuling Feng Hongwei Jiao Youlin Shang |
| author_facet | Hongwu Li Yuling Feng Hongwei Jiao Youlin Shang |
| author_sort | Hongwu Li |
| collection | DOAJ |
| description | By using the outer space branch-and-reduction scheme, we present a novel algorithm for globally optimizing the sum of several affine fractional functions problem (SAFFP) over a nonempty compact set. For providing the reliable lower bounds in the searching process of iterations, we devise a novel linearizing method to establish the affine relaxation problem (ARP) for the SAFFP. Thus, the main computational work involves solving a series of ARP. For improving the convergence speed of the algorithm, an outer space region reduction technique is proposed by utilizing the objective function characteristics. Through computational complexity analysis, we estimate the algorithmic maximum iteration times. Finally, numerical comparison results are given to reveal the algorithmic computational advantages. |
| first_indexed | 2024-04-10T06:06:19Z |
| format | Article |
| id | doaj.art-9408fcf46247403e82e78c43a4bf7663 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-10T06:06:19Z |
| publishDate | 2023-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-9408fcf46247403e82e78c43a4bf76632023-03-03T01:18:34ZengAIMS PressAIMS Mathematics2473-69882023-02-01849247926410.3934/math.2023464A novel algorithm for solving sum of several affine fractional functionsHongwu Li 0Yuling Feng1Hongwei Jiao2Youlin Shang 31. School of Science, Beijing University of Technology, Beijing 100124, China 2. School of Mathematics and Statistics, Nanyang Normal University, Nanyang 473061, China3. School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang 453003, China3. School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang 453003, China 4. Postdoctoral Research Station of Control Science and Engineering, Henan University of Science and Technology, Luoyang 471023, China4. Postdoctoral Research Station of Control Science and Engineering, Henan University of Science and Technology, Luoyang 471023, ChinaBy using the outer space branch-and-reduction scheme, we present a novel algorithm for globally optimizing the sum of several affine fractional functions problem (SAFFP) over a nonempty compact set. For providing the reliable lower bounds in the searching process of iterations, we devise a novel linearizing method to establish the affine relaxation problem (ARP) for the SAFFP. Thus, the main computational work involves solving a series of ARP. For improving the convergence speed of the algorithm, an outer space region reduction technique is proposed by utilizing the objective function characteristics. Through computational complexity analysis, we estimate the algorithmic maximum iteration times. Finally, numerical comparison results are given to reveal the algorithmic computational advantages.https://www.aimspress.com/article/doi/10.3934/math.2023464?viewType=HTMLsum of several affine fractional functionsbranch-and-reductionaffine relaxation problemouter space region reduction techniquecomputational complexity |
| spellingShingle | Hongwu Li Yuling Feng Hongwei Jiao Youlin Shang A novel algorithm for solving sum of several affine fractional functions AIMS Mathematics sum of several affine fractional functions branch-and-reduction affine relaxation problem outer space region reduction technique computational complexity |
| title | A novel algorithm for solving sum of several affine fractional functions |
| title_full | A novel algorithm for solving sum of several affine fractional functions |
| title_fullStr | A novel algorithm for solving sum of several affine fractional functions |
| title_full_unstemmed | A novel algorithm for solving sum of several affine fractional functions |
| title_short | A novel algorithm for solving sum of several affine fractional functions |
| title_sort | novel algorithm for solving sum of several affine fractional functions |
| topic | sum of several affine fractional functions branch-and-reduction affine relaxation problem outer space region reduction technique computational complexity |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023464?viewType=HTML |
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