A nonmonotone trust region technique with active-set and interior-point methods to solve nonlinearly constrained optimization problems
This study is devoted to incorporating a nonmonotone strategy with an automatically adjusted trust-region radius to propose a more efficient hybrid of trust-region approaches for constrained optimization problems. First, the active-set strategy was used with a penalty and Newton's interior poin...
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| Format: | Article |
| Language: | English |
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AIMS Press
2025-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025117 |
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| author | Bothina El-Sobky Yousria Abo-Elnaga Gehan Ashry |
| author_facet | Bothina El-Sobky Yousria Abo-Elnaga Gehan Ashry |
| author_sort | Bothina El-Sobky |
| collection | DOAJ |
| description | This study is devoted to incorporating a nonmonotone strategy with an automatically adjusted trust-region radius to propose a more efficient hybrid of trust-region approaches for constrained optimization problems. First, the active-set strategy was used with a penalty and Newton's interior point method to convert a nonlinearly constrained optimization problem to an equivalent nonlinear unconstrained optimization problem. Second, a nonmonotone trust region was utilized to guarantee convergence from any starting point to the stationary point. Third, a global convergence theory for the proposed algorithm was presented under some assumptions. Finally, the proposed algorithm was tested by well-known test problems (the CUTE collection); three engineering design problems were resolved, and the results were compared with those of other respected optimizers. Based on the results, the suggested approach generally provides better approximation solutions and requires fewer iterations than the other algorithms under consideration. The performance of the proposed algorithm was also investigated, and computational results clarified that the suggested algorithm was competitive and better than other optimization algorithms. |
| format | Article |
| id | doaj-art-8316748fd4ea4cc0aa2bf2cd855fb5b6 |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-8316748fd4ea4cc0aa2bf2cd855fb5b62025-08-20T02:26:19ZengAIMS PressAIMS Mathematics2473-69882025-02-011022509254010.3934/math.2025117A nonmonotone trust region technique with active-set and interior-point methods to solve nonlinearly constrained optimization problemsBothina El-Sobky0Yousria Abo-Elnaga1Gehan Ashry2Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, EgyptDepartment of basic science, Tenth of Ramadan City, Higher Technological Institute, EgyptDepartment of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, EgyptThis study is devoted to incorporating a nonmonotone strategy with an automatically adjusted trust-region radius to propose a more efficient hybrid of trust-region approaches for constrained optimization problems. First, the active-set strategy was used with a penalty and Newton's interior point method to convert a nonlinearly constrained optimization problem to an equivalent nonlinear unconstrained optimization problem. Second, a nonmonotone trust region was utilized to guarantee convergence from any starting point to the stationary point. Third, a global convergence theory for the proposed algorithm was presented under some assumptions. Finally, the proposed algorithm was tested by well-known test problems (the CUTE collection); three engineering design problems were resolved, and the results were compared with those of other respected optimizers. Based on the results, the suggested approach generally provides better approximation solutions and requires fewer iterations than the other algorithms under consideration. The performance of the proposed algorithm was also investigated, and computational results clarified that the suggested algorithm was competitive and better than other optimization algorithms.https://www.aimspress.com/article/doi/10.3934/math.2025117active setpenalty methodinterior pointnonmonotone trust regionglobal convergence |
| spellingShingle | Bothina El-Sobky Yousria Abo-Elnaga Gehan Ashry A nonmonotone trust region technique with active-set and interior-point methods to solve nonlinearly constrained optimization problems AIMS Mathematics active set penalty method interior point nonmonotone trust region global convergence |
| title | A nonmonotone trust region technique with active-set and interior-point methods to solve nonlinearly constrained optimization problems |
| title_full | A nonmonotone trust region technique with active-set and interior-point methods to solve nonlinearly constrained optimization problems |
| title_fullStr | A nonmonotone trust region technique with active-set and interior-point methods to solve nonlinearly constrained optimization problems |
| title_full_unstemmed | A nonmonotone trust region technique with active-set and interior-point methods to solve nonlinearly constrained optimization problems |
| title_short | A nonmonotone trust region technique with active-set and interior-point methods to solve nonlinearly constrained optimization problems |
| title_sort | nonmonotone trust region technique with active set and interior point methods to solve nonlinearly constrained optimization problems |
| topic | active set penalty method interior point nonmonotone trust region global convergence |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025117 |
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