A Superlinearly Convergent Penalty Method with Nonsmooth Line Search for Constrained Nonlinear Least Squares
Recently, we have presented a projected structured algorithm for solving constrained nonlinear least squares problems, and established its local two-step Q-superlinear convergence. The approach is based on an adaptive structured scheme due to Mahdavi-Amiri and Bartels of the exact penalty method. Th...
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| Format: | Article |
| Language: | English |
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Sultan Qaboos University
2012-04-01
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| Series: | Sultan Qaboos University Journal for Science |
| Subjects: | |
| Online Access: | https://journals.squ.edu.om/index.php/squjs/article/view/390 |
| _version_ | 1818559334928351232 |
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| author | Nezam Mahdavi-Amiri Mohammad Reza Ansari |
| author_facet | Nezam Mahdavi-Amiri Mohammad Reza Ansari |
| author_sort | Nezam Mahdavi-Amiri |
| collection | DOAJ |
| description | Recently, we have presented a projected structured algorithm for solving constrained nonlinear least squares problems, and established its local two-step Q-superlinear convergence. The approach is based on an adaptive structured scheme due to Mahdavi-Amiri and Bartels of the exact penalty method. The structured adaptation also makes use of the ideas of Nocedal and Overton for handling the quasi-Newton updates of projected Hessians and appropriates the structuring scheme of Dennis, Martinez and Tapia. Here, for robustness, we present a specific nonsmooth line search strategy, taking account of the least squares objective. We also discuss the details of our new nonsmooth line search strategy, implementation details of the algorithm, and provide comparative results obtained by the testing of our program and three nonlinear programming codes from KNITRO on test problems (both small and large residuals) from Hock and Schittkowski, Lukšan and Vlček and some randomly generated ones due to Bartels and Mahdavi-Amiri. The results indeed affirm the practical relevance of our special considerations for the inherent structure of the least squares. |
| first_indexed | 2024-12-14T00:24:04Z |
| format | Article |
| id | doaj.art-ca4585b7fce345cdae8c69d459764caa |
| institution | Directory Open Access Journal |
| issn | 1027-524X 2414-536X |
| language | English |
| last_indexed | 2024-12-14T00:24:04Z |
| publishDate | 2012-04-01 |
| publisher | Sultan Qaboos University |
| record_format | Article |
| series | Sultan Qaboos University Journal for Science |
| spelling | doaj.art-ca4585b7fce345cdae8c69d459764caa2022-12-21T23:25:06ZengSultan Qaboos UniversitySultan Qaboos University Journal for Science1027-524X2414-536X2012-04-0117110312410.24200/squjs.vol17iss1pp103-124387A Superlinearly Convergent Penalty Method with Nonsmooth Line Search for Constrained Nonlinear Least SquaresNezam Mahdavi-Amiri0Mohammad Reza Ansari1Faculty of Mathematical Sciences, Sharif University of Technology, Tehran, IranFaculty of Mathematical Sciences, Sharif University of Technology, Tehran, IranRecently, we have presented a projected structured algorithm for solving constrained nonlinear least squares problems, and established its local two-step Q-superlinear convergence. The approach is based on an adaptive structured scheme due to Mahdavi-Amiri and Bartels of the exact penalty method. The structured adaptation also makes use of the ideas of Nocedal and Overton for handling the quasi-Newton updates of projected Hessians and appropriates the structuring scheme of Dennis, Martinez and Tapia. Here, for robustness, we present a specific nonsmooth line search strategy, taking account of the least squares objective. We also discuss the details of our new nonsmooth line search strategy, implementation details of the algorithm, and provide comparative results obtained by the testing of our program and three nonlinear programming codes from KNITRO on test problems (both small and large residuals) from Hock and Schittkowski, Lukšan and Vlček and some randomly generated ones due to Bartels and Mahdavi-Amiri. The results indeed affirm the practical relevance of our special considerations for the inherent structure of the least squares.https://journals.squ.edu.om/index.php/squjs/article/view/390Constrained nonlinear programming, Exact penalty method, Nonlinear least squares. Nonsmooth line search, Projected structured Hessian update. |
| spellingShingle | Nezam Mahdavi-Amiri Mohammad Reza Ansari A Superlinearly Convergent Penalty Method with Nonsmooth Line Search for Constrained Nonlinear Least Squares Sultan Qaboos University Journal for Science Constrained nonlinear programming, Exact penalty method, Nonlinear least squares. Nonsmooth line search, Projected structured Hessian update. |
| title | A Superlinearly Convergent Penalty Method with Nonsmooth Line Search for Constrained Nonlinear Least Squares |
| title_full | A Superlinearly Convergent Penalty Method with Nonsmooth Line Search for Constrained Nonlinear Least Squares |
| title_fullStr | A Superlinearly Convergent Penalty Method with Nonsmooth Line Search for Constrained Nonlinear Least Squares |
| title_full_unstemmed | A Superlinearly Convergent Penalty Method with Nonsmooth Line Search for Constrained Nonlinear Least Squares |
| title_short | A Superlinearly Convergent Penalty Method with Nonsmooth Line Search for Constrained Nonlinear Least Squares |
| title_sort | superlinearly convergent penalty method with nonsmooth line search for constrained nonlinear least squares |
| topic | Constrained nonlinear programming, Exact penalty method, Nonlinear least squares. Nonsmooth line search, Projected structured Hessian update. |
| url | https://journals.squ.edu.om/index.php/squjs/article/view/390 |
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