Two-Phase Generalized Reduced Gradient Method for Constrained Global Optimization
The random perturbation of generalized reduced gradient method for optimization under nonlinear differentiable constraints is proposed. Generally speaking, a particular iteration of this method proceeds in two phases. In the Restoration Phase, feasibility is restored by means of the resolution of an...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2010/976529 |
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| author | Abdelkrim El Mouatasim |
| author_facet | Abdelkrim El Mouatasim |
| author_sort | Abdelkrim El Mouatasim |
| collection | DOAJ |
| description | The random perturbation of generalized reduced gradient method for optimization under nonlinear differentiable constraints is proposed. Generally speaking, a particular iteration of this method proceeds in two phases. In the Restoration Phase, feasibility is restored by means of the resolution of an auxiliary nonlinear problem, a generally nonlinear system of equations. In the Optimization Phase, optimality is improved by means of the consideration of the objective function, on the tangent subspace to the constraints. In this paper, optimal assumptions are stated on the Restoration Phase and the Optimization Phase that establish the global convergence of the algorithm. Some numerical examples are also given by mixture problem and octagon problem. |
| format | Article |
| id | doaj-art-31ae8437e2d94cca8c41b9a544cd6c54 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-31ae8437e2d94cca8c41b9a544cd6c542025-02-03T06:12:19ZengWileyJournal of Applied Mathematics1110-757X1687-00422010-01-01201010.1155/2010/976529976529Two-Phase Generalized Reduced Gradient Method for Constrained Global OptimizationAbdelkrim El Mouatasim0Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan, Saudi ArabiaThe random perturbation of generalized reduced gradient method for optimization under nonlinear differentiable constraints is proposed. Generally speaking, a particular iteration of this method proceeds in two phases. In the Restoration Phase, feasibility is restored by means of the resolution of an auxiliary nonlinear problem, a generally nonlinear system of equations. In the Optimization Phase, optimality is improved by means of the consideration of the objective function, on the tangent subspace to the constraints. In this paper, optimal assumptions are stated on the Restoration Phase and the Optimization Phase that establish the global convergence of the algorithm. Some numerical examples are also given by mixture problem and octagon problem.http://dx.doi.org/10.1155/2010/976529 |
| spellingShingle | Abdelkrim El Mouatasim Two-Phase Generalized Reduced Gradient Method for Constrained Global Optimization Journal of Applied Mathematics |
| title | Two-Phase Generalized Reduced Gradient Method for Constrained Global Optimization |
| title_full | Two-Phase Generalized Reduced Gradient Method for Constrained Global Optimization |
| title_fullStr | Two-Phase Generalized Reduced Gradient Method for Constrained Global Optimization |
| title_full_unstemmed | Two-Phase Generalized Reduced Gradient Method for Constrained Global Optimization |
| title_short | Two-Phase Generalized Reduced Gradient Method for Constrained Global Optimization |
| title_sort | two phase generalized reduced gradient method for constrained global optimization |
| url | http://dx.doi.org/10.1155/2010/976529 |
| work_keys_str_mv | AT abdelkrimelmouatasim twophasegeneralizedreducedgradientmethodforconstrainedglobaloptimization |