Combining non-Monotone trust rregion method with a new adaptive radius for unconstrained optimization problems
Purpose: One of the most effective methods for solving unconstrained optimization problems is the trust region method. The strategy of determining the radius of the trust region has a significant effect on the efficiency of this method. On the other hand, imposing the monotonicity condition will dec...
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| Format: | Article |
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Ayandegan Institute of Higher Education, Tonekabon,
2024-06-01
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| Series: | تصمیم گیری و تحقیق در عملیات |
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| Online Access: | https://www.journal-dmor.ir/article_173105_25a81673e0bd4ca843735869cf0aac1f.pdf |
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| author | Seyed Hamzeh Mirzaei Ali Ashrafi |
| author_facet | Seyed Hamzeh Mirzaei Ali Ashrafi |
| author_sort | Seyed Hamzeh Mirzaei |
| collection | DOAJ |
| description | Purpose: One of the most effective methods for solving unconstrained optimization problems is the trust region method. The strategy of determining the radius of the trust region has a significant effect on the efficiency of this method. On the other hand, imposing the monotonicity condition will decrease the convergence speed of this method. Therefore, improving and increasing the efficiency of this method is one of the most important issues and the attention of researchers.Methodology: Establishing a new adaptive trust region radius as well as combining the trust region method with a non-monotone strategy to avoid the adverse effects of monotonocity.Findings: A new adaptive trust region radius converged to zero is provided, and then a trust region combination is performed using a non-monotone strategy. Running the algorithm on a set of test functions shows that the new adaptive radius, along with the non-monotone strategy used, significantly improves the efficiency of the trust region method.Originality/Value: The presented non-monotone adaptive algorithm has a second-order convergence rate. In addition, it significantly reduces computational costs compared to traditional algorithms. On the other hand, the new adaptive radius avoids the ineffectiveness of the trust region close to the solution. |
| format | Article |
| id | doaj-art-6b03e1dc118043de841bf768771d2d1b |
| institution | Kabale University |
| issn | 2538-5097 2676-6159 |
| language | fas |
| publishDate | 2024-06-01 |
| publisher | Ayandegan Institute of Higher Education, Tonekabon, |
| record_format | Article |
| series | تصمیم گیری و تحقیق در عملیات |
| spelling | doaj-art-6b03e1dc118043de841bf768771d2d1b2025-01-30T15:03:40ZfasAyandegan Institute of Higher Education, Tonekabon,تصمیم گیری و تحقیق در عملیات2538-50972676-61592024-06-0191304110.22105/dmor.2023.368847.1686173105Combining non-Monotone trust rregion method with a new adaptive radius for unconstrained optimization problemsSeyed Hamzeh Mirzaei0Ali Ashrafi1Department of Mathematics, Semnan University, Semnan, Iran.Department of Mathematics, Semnan University, Semnan, Iran.Purpose: One of the most effective methods for solving unconstrained optimization problems is the trust region method. The strategy of determining the radius of the trust region has a significant effect on the efficiency of this method. On the other hand, imposing the monotonicity condition will decrease the convergence speed of this method. Therefore, improving and increasing the efficiency of this method is one of the most important issues and the attention of researchers.Methodology: Establishing a new adaptive trust region radius as well as combining the trust region method with a non-monotone strategy to avoid the adverse effects of monotonocity.Findings: A new adaptive trust region radius converged to zero is provided, and then a trust region combination is performed using a non-monotone strategy. Running the algorithm on a set of test functions shows that the new adaptive radius, along with the non-monotone strategy used, significantly improves the efficiency of the trust region method.Originality/Value: The presented non-monotone adaptive algorithm has a second-order convergence rate. In addition, it significantly reduces computational costs compared to traditional algorithms. On the other hand, the new adaptive radius avoids the ineffectiveness of the trust region close to the solution.https://www.journal-dmor.ir/article_173105_25a81673e0bd4ca843735869cf0aac1f.pdfnon-monotone strategyunconstrained optimizationtrust regionglobal convergence |
| spellingShingle | Seyed Hamzeh Mirzaei Ali Ashrafi Combining non-Monotone trust rregion method with a new adaptive radius for unconstrained optimization problems تصمیم گیری و تحقیق در عملیات non-monotone strategy unconstrained optimization trust region global convergence |
| title | Combining non-Monotone trust rregion method with a new adaptive radius for unconstrained optimization problems |
| title_full | Combining non-Monotone trust rregion method with a new adaptive radius for unconstrained optimization problems |
| title_fullStr | Combining non-Monotone trust rregion method with a new adaptive radius for unconstrained optimization problems |
| title_full_unstemmed | Combining non-Monotone trust rregion method with a new adaptive radius for unconstrained optimization problems |
| title_short | Combining non-Monotone trust rregion method with a new adaptive radius for unconstrained optimization problems |
| title_sort | combining non monotone trust rregion method with a new adaptive radius for unconstrained optimization problems |
| topic | non-monotone strategy unconstrained optimization trust region global convergence |
| url | https://www.journal-dmor.ir/article_173105_25a81673e0bd4ca843735869cf0aac1f.pdf |
| work_keys_str_mv | AT seyedhamzehmirzaei combiningnonmonotonetrustrregionmethodwithanewadaptiveradiusforunconstrainedoptimizationproblems AT aliashrafi combiningnonmonotonetrustrregionmethodwithanewadaptiveradiusforunconstrainedoptimizationproblems |