Newton-Krylov Type Algorithm for Solving Nonlinear Least Squares Problems
The minimization of a quadratic function within an ellipsoidal trust region is an important subproblem for many nonlinear programming algorithms. When the number of variables is large, one of the most widely used strategies is to project the original problem into a small dimensional subspace. In thi...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2009/435851 |
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| _version_ | 1850168164298522624 |
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| author | Mohammedi R. Abdel-Aziz Mahmoud M. El-Alem |
| author_facet | Mohammedi R. Abdel-Aziz Mahmoud M. El-Alem |
| author_sort | Mohammedi R. Abdel-Aziz |
| collection | DOAJ |
| description | The minimization of a quadratic function within an ellipsoidal trust region is an important
subproblem for many nonlinear programming algorithms. When the number of variables is large,
one of the most widely used strategies is to project the original problem into a small dimensional
subspace. In this paper, we introduce an algorithm for solving nonlinear least squares problems.
This algorithm is based on constructing a basis for the Krylov subspace in conjunction with a
model trust region technique to choose the step. The computational step on the small dimensional
subspace lies inside the trust region. The Krylov subspace is terminated such that the termination
condition allows the gradient to be decreased on it. A convergence theory of this algorithm is
presented. It is shown that this algorithm is globally convergent. |
| format | Article |
| id | doaj-art-e61453b7dc1a4798b5e706b5427e3a08 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e61453b7dc1a4798b5e706b5427e3a082025-08-20T02:21:02ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252009-01-01200910.1155/2009/435851435851Newton-Krylov Type Algorithm for Solving Nonlinear Least Squares ProblemsMohammedi R. Abdel-Aziz0Mahmoud M. El-Alem1Department of Mathematics and Computer Science, Faculty of Science, Kuwait University, P.O. 5969, Safat 13060, Kuwait City, KuwaitDepartment of Mathematics and Computer Science, Faculty of Science, Kuwait University, P.O. 5969, Safat 13060, Kuwait City, KuwaitThe minimization of a quadratic function within an ellipsoidal trust region is an important subproblem for many nonlinear programming algorithms. When the number of variables is large, one of the most widely used strategies is to project the original problem into a small dimensional subspace. In this paper, we introduce an algorithm for solving nonlinear least squares problems. This algorithm is based on constructing a basis for the Krylov subspace in conjunction with a model trust region technique to choose the step. The computational step on the small dimensional subspace lies inside the trust region. The Krylov subspace is terminated such that the termination condition allows the gradient to be decreased on it. A convergence theory of this algorithm is presented. It is shown that this algorithm is globally convergent.http://dx.doi.org/10.1155/2009/435851 |
| spellingShingle | Mohammedi R. Abdel-Aziz Mahmoud M. El-Alem Newton-Krylov Type Algorithm for Solving Nonlinear Least Squares Problems International Journal of Mathematics and Mathematical Sciences |
| title | Newton-Krylov Type Algorithm for Solving Nonlinear Least Squares Problems |
| title_full | Newton-Krylov Type Algorithm for Solving Nonlinear Least Squares Problems |
| title_fullStr | Newton-Krylov Type Algorithm for Solving Nonlinear Least Squares Problems |
| title_full_unstemmed | Newton-Krylov Type Algorithm for Solving Nonlinear Least Squares Problems |
| title_short | Newton-Krylov Type Algorithm for Solving Nonlinear Least Squares Problems |
| title_sort | newton krylov type algorithm for solving nonlinear least squares problems |
| url | http://dx.doi.org/10.1155/2009/435851 |
| work_keys_str_mv | AT mohammedirabdelaziz newtonkrylovtypealgorithmforsolvingnonlinearleastsquaresproblems AT mahmoudmelalem newtonkrylovtypealgorithmforsolvingnonlinearleastsquaresproblems |