Inexact Exponential Penalty Function with the Augmented Lagrangian for Multiobjective Optimization Algorithms
This paper uses an augmented Lagrangian method based on an inexact exponential penalty function to solve constrained multiobjective optimization problems. Two algorithms have been proposed in this study. The first algorithm uses a projected gradient, while the second uses the steepest descent method...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/9615743 |
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| author | Appolinaire Tougma Kounhinir Some |
| author_facet | Appolinaire Tougma Kounhinir Some |
| author_sort | Appolinaire Tougma |
| collection | DOAJ |
| description | This paper uses an augmented Lagrangian method based on an inexact exponential penalty function to solve constrained multiobjective optimization problems. Two algorithms have been proposed in this study. The first algorithm uses a projected gradient, while the second uses the steepest descent method. By these algorithms, we have been able to generate a set of nondominated points that approximate the Pareto optimal solutions of the initial problem. Some proofs of theoretical convergence are also proposed for two different criteria for the set of generated stationary Pareto points. In addition, we compared our method with the NSGA-II and augmented the Lagrangian cone method on some test problems from the literature. A numerical analysis of the obtained solutions indicates that our method is competitive with regard to the test problems used for the comparison. |
| format | Article |
| id | doaj-art-c118983d985c4c3a8205be232010f36a |
| institution | Kabale University |
| issn | 1687-0042 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-c118983d985c4c3a8205be232010f36a2025-02-03T05:32:36ZengWileyJournal of Applied Mathematics1687-00422024-01-01202410.1155/2024/9615743Inexact Exponential Penalty Function with the Augmented Lagrangian for Multiobjective Optimization AlgorithmsAppolinaire Tougma0Kounhinir Some1Department of MathematicsDepartment of MathematicsThis paper uses an augmented Lagrangian method based on an inexact exponential penalty function to solve constrained multiobjective optimization problems. Two algorithms have been proposed in this study. The first algorithm uses a projected gradient, while the second uses the steepest descent method. By these algorithms, we have been able to generate a set of nondominated points that approximate the Pareto optimal solutions of the initial problem. Some proofs of theoretical convergence are also proposed for two different criteria for the set of generated stationary Pareto points. In addition, we compared our method with the NSGA-II and augmented the Lagrangian cone method on some test problems from the literature. A numerical analysis of the obtained solutions indicates that our method is competitive with regard to the test problems used for the comparison.http://dx.doi.org/10.1155/2024/9615743 |
| spellingShingle | Appolinaire Tougma Kounhinir Some Inexact Exponential Penalty Function with the Augmented Lagrangian for Multiobjective Optimization Algorithms Journal of Applied Mathematics |
| title | Inexact Exponential Penalty Function with the Augmented Lagrangian for Multiobjective Optimization Algorithms |
| title_full | Inexact Exponential Penalty Function with the Augmented Lagrangian for Multiobjective Optimization Algorithms |
| title_fullStr | Inexact Exponential Penalty Function with the Augmented Lagrangian for Multiobjective Optimization Algorithms |
| title_full_unstemmed | Inexact Exponential Penalty Function with the Augmented Lagrangian for Multiobjective Optimization Algorithms |
| title_short | Inexact Exponential Penalty Function with the Augmented Lagrangian for Multiobjective Optimization Algorithms |
| title_sort | inexact exponential penalty function with the augmented lagrangian for multiobjective optimization algorithms |
| url | http://dx.doi.org/10.1155/2024/9615743 |
| work_keys_str_mv | AT appolinairetougma inexactexponentialpenaltyfunctionwiththeaugmentedlagrangianformultiobjectiveoptimizationalgorithms AT kounhinirsome inexactexponentialpenaltyfunctionwiththeaugmentedlagrangianformultiobjectiveoptimizationalgorithms |