A nonmonotone trust-region-approach with nonmonotone adaptive radius for solving nonlinear systems
This paper presents a trust-region procedure for solving systems of nonlinear equations. The proposed approach takes advantages of an effective adaptive trust-region radius and a nonmonotone strategy by combining both of them appropriately. It is believed that selecting an appropriate adaptive radiu...
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| Format: | Article |
| Language: | English |
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Ferdowsi University of Mashhad
2016-02-01
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| Series: | Iranian Journal of Numerical Analysis and Optimization |
| Subjects: | |
| Online Access: | https://ijnao.um.ac.ir/article_24467_1ba15f55057e5082b16ff3da82728819.pdf |
| _version_ | 1819100583532953600 |
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| author | Keyvan Amini Hamid Esmaeili Morteza Kimiaei |
| author_facet | Keyvan Amini Hamid Esmaeili Morteza Kimiaei |
| author_sort | Keyvan Amini |
| collection | DOAJ |
| description | This paper presents a trust-region procedure for solving systems of nonlinear equations. The proposed approach takes advantages of an effective adaptive trust-region radius and a nonmonotone strategy by combining both of them appropriately. It is believed that selecting an appropriate adaptive radius based on a suitable nonmonotone strategy can improve the efficiency and robustness of the trust-region framework as well as can decrease the computational cost of the algorithm by decreasing the number of subproblems that must be solved. The global convergence to first order stationary points as well as the local q-quadratic convergence of the proposed approach are proved. Numerical experiments show that the new algorithm is promising and attractive for solving nonlinear systems. |
| first_indexed | 2024-12-22T01:05:05Z |
| format | Article |
| id | doaj.art-0bb10e45793646a6950b2596d3b28111 |
| institution | Directory Open Access Journal |
| issn | 2423-6977 2423-6969 |
| language | English |
| last_indexed | 2024-12-22T01:05:05Z |
| publishDate | 2016-02-01 |
| publisher | Ferdowsi University of Mashhad |
| record_format | Article |
| series | Iranian Journal of Numerical Analysis and Optimization |
| spelling | doaj.art-0bb10e45793646a6950b2596d3b281112022-12-21T18:44:06ZengFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69772423-69692016-02-016110112110.22067/ijnao.v6i1.4560724467A nonmonotone trust-region-approach with nonmonotone adaptive radius for solving nonlinear systemsKeyvan Amini0Hamid Esmaeili1Morteza Kimiaei2Razi UniversityBu-Ali Sina University,Department of Mathematics, Asadabad Branch, Islamic Azad University, Asadabad, Iran.This paper presents a trust-region procedure for solving systems of nonlinear equations. The proposed approach takes advantages of an effective adaptive trust-region radius and a nonmonotone strategy by combining both of them appropriately. It is believed that selecting an appropriate adaptive radius based on a suitable nonmonotone strategy can improve the efficiency and robustness of the trust-region framework as well as can decrease the computational cost of the algorithm by decreasing the number of subproblems that must be solved. The global convergence to first order stationary points as well as the local q-quadratic convergence of the proposed approach are proved. Numerical experiments show that the new algorithm is promising and attractive for solving nonlinear systems.https://ijnao.um.ac.ir/article_24467_1ba15f55057e5082b16ff3da82728819.pdfnonlinear equationstrust-region frameworkadaptive radiusnonmonotone technique |
| spellingShingle | Keyvan Amini Hamid Esmaeili Morteza Kimiaei A nonmonotone trust-region-approach with nonmonotone adaptive radius for solving nonlinear systems Iranian Journal of Numerical Analysis and Optimization nonlinear equations trust-region framework adaptive radius nonmonotone technique |
| title | A nonmonotone trust-region-approach with nonmonotone adaptive radius for solving nonlinear systems |
| title_full | A nonmonotone trust-region-approach with nonmonotone adaptive radius for solving nonlinear systems |
| title_fullStr | A nonmonotone trust-region-approach with nonmonotone adaptive radius for solving nonlinear systems |
| title_full_unstemmed | A nonmonotone trust-region-approach with nonmonotone adaptive radius for solving nonlinear systems |
| title_short | A nonmonotone trust-region-approach with nonmonotone adaptive radius for solving nonlinear systems |
| title_sort | nonmonotone trust region approach with nonmonotone adaptive radius for solving nonlinear systems |
| topic | nonlinear equations trust-region framework adaptive radius nonmonotone technique |
| url | https://ijnao.um.ac.ir/article_24467_1ba15f55057e5082b16ff3da82728819.pdf |
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