RPCGB Method for Large-Scale Global Optimization Problems
In this paper, we propose a new approach for optimizing a large-scale non-convex differentiable function subject to linear equality constraints. The proposed method, RPCGB (random perturbation of the conditional gradient method with bisection algorithm), computes a search direction by the conditiona...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/6/603 |
| _version_ | 1797596121809289216 |
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| author | Abderrahmane Ettahiri Abdelkrim El Mouatasim |
| author_facet | Abderrahmane Ettahiri Abdelkrim El Mouatasim |
| author_sort | Abderrahmane Ettahiri |
| collection | DOAJ |
| description | In this paper, we propose a new approach for optimizing a large-scale non-convex differentiable function subject to linear equality constraints. The proposed method, RPCGB (random perturbation of the conditional gradient method with bisection algorithm), computes a search direction by the conditional gradient, and an optimal line search is found by a bisection algorithm, which results in a decrease of the cost function. The RPCGB method is designed to guarantee global convergence of the algorithm. An implementation and testing of the method are given, with numerical results of large-scale problems that demonstrate its efficiency. |
| first_indexed | 2024-03-11T02:47:04Z |
| format | Article |
| id | doaj.art-bae8ef3c395541ab9fd826f8b63c6e67 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T02:47:04Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-bae8ef3c395541ab9fd826f8b63c6e672023-11-18T09:17:21ZengMDPI AGAxioms2075-16802023-06-0112660310.3390/axioms12060603RPCGB Method for Large-Scale Global Optimization ProblemsAbderrahmane Ettahiri0Abdelkrim El Mouatasim1Laboratory LABSI, Faculty of Sciences Agadir (FSA), Ibnou Zohr University, B.P. 8106, Agadir 80000, MoroccoDepartment of Mathematics and Management, Faculty of Polydisciplinary Ouarzazate (FPO), Ibnou Zohr University, B.P. 284, Ouarzazate 45800, MoroccoIn this paper, we propose a new approach for optimizing a large-scale non-convex differentiable function subject to linear equality constraints. The proposed method, RPCGB (random perturbation of the conditional gradient method with bisection algorithm), computes a search direction by the conditional gradient, and an optimal line search is found by a bisection algorithm, which results in a decrease of the cost function. The RPCGB method is designed to guarantee global convergence of the algorithm. An implementation and testing of the method are given, with numerical results of large-scale problems that demonstrate its efficiency.https://www.mdpi.com/2075-1680/12/6/603non-convex optimizationlarge-scale problemconditional gradient methodbisection algorithmrandom perturbation |
| spellingShingle | Abderrahmane Ettahiri Abdelkrim El Mouatasim RPCGB Method for Large-Scale Global Optimization Problems Axioms non-convex optimization large-scale problem conditional gradient method bisection algorithm random perturbation |
| title | RPCGB Method for Large-Scale Global Optimization Problems |
| title_full | RPCGB Method for Large-Scale Global Optimization Problems |
| title_fullStr | RPCGB Method for Large-Scale Global Optimization Problems |
| title_full_unstemmed | RPCGB Method for Large-Scale Global Optimization Problems |
| title_short | RPCGB Method for Large-Scale Global Optimization Problems |
| title_sort | rpcgb method for large scale global optimization problems |
| topic | non-convex optimization large-scale problem conditional gradient method bisection algorithm random perturbation |
| url | https://www.mdpi.com/2075-1680/12/6/603 |
| work_keys_str_mv | AT abderrahmaneettahiri rpcgbmethodforlargescaleglobaloptimizationproblems AT abdelkrimelmouatasim rpcgbmethodforlargescaleglobaloptimizationproblems |