A redistributed cutting plane bundle-type algorithm for multiobjective nonsmooth optimization
I construct a new cutting-plane model for approximating nonsmooth nonconvex functions in multiobjective optimization and propose a new bundle-type method with the help of an improvement function. The presented bundle method possesses three features. Firstly, the objective and constraint functions ar...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-05-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022710?viewType=HTML |
| _version_ | 1818203414093365248 |
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| author | Jia-Tong Li |
| author_facet | Jia-Tong Li |
| author_sort | Jia-Tong Li |
| collection | DOAJ |
| description | I construct a new cutting-plane model for approximating nonsmooth nonconvex functions in multiobjective optimization and propose a new bundle-type method with the help of an improvement function. The presented bundle method possesses three features. Firstly, the objective and constraint functions are approximated by a new cutting-plane model, which is a local convexification of the corresponding functions, instead of the entire approximation for the functions, as most bundle methods do. Secondly, the subgradients and values of the objective and constraint functions are computed approximately. In other words, approximate calculation is applied to the method, and the proposed algorithm is doubly approximate to some extent. Thirdly, the introduction of the improvement function eliminates the necessity of employing any scalarization, which is the usual method when dealing with multiobjective optimization. Under reasonable conditions satisfactory convergence results are obtained. |
| first_indexed | 2024-12-12T03:24:58Z |
| format | Article |
| id | doaj.art-665e46af684c4edca7586e47cccf832f |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-12T03:24:58Z |
| publishDate | 2022-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-665e46af684c4edca7586e47cccf832f2022-12-22T00:40:04ZengAIMS PressAIMS Mathematics2473-69882022-05-0177128271284110.3934/math.2022710A redistributed cutting plane bundle-type algorithm for multiobjective nonsmooth optimizationJia-Tong Li 0 College of Science, Northeast Forestry University, Harbin 150040, ChinaI construct a new cutting-plane model for approximating nonsmooth nonconvex functions in multiobjective optimization and propose a new bundle-type method with the help of an improvement function. The presented bundle method possesses three features. Firstly, the objective and constraint functions are approximated by a new cutting-plane model, which is a local convexification of the corresponding functions, instead of the entire approximation for the functions, as most bundle methods do. Secondly, the subgradients and values of the objective and constraint functions are computed approximately. In other words, approximate calculation is applied to the method, and the proposed algorithm is doubly approximate to some extent. Thirdly, the introduction of the improvement function eliminates the necessity of employing any scalarization, which is the usual method when dealing with multiobjective optimization. Under reasonable conditions satisfactory convergence results are obtained.https://www.aimspress.com/article/doi/10.3934/math.2022710?viewType=HTMLmultiobjective nonsmooth optimizationcutting-plane modelredistributed bundle methodapproximate calculationsubgradient |
| spellingShingle | Jia-Tong Li A redistributed cutting plane bundle-type algorithm for multiobjective nonsmooth optimization AIMS Mathematics multiobjective nonsmooth optimization cutting-plane model redistributed bundle method approximate calculation subgradient |
| title | A redistributed cutting plane bundle-type algorithm for multiobjective nonsmooth optimization |
| title_full | A redistributed cutting plane bundle-type algorithm for multiobjective nonsmooth optimization |
| title_fullStr | A redistributed cutting plane bundle-type algorithm for multiobjective nonsmooth optimization |
| title_full_unstemmed | A redistributed cutting plane bundle-type algorithm for multiobjective nonsmooth optimization |
| title_short | A redistributed cutting plane bundle-type algorithm for multiobjective nonsmooth optimization |
| title_sort | redistributed cutting plane bundle type algorithm for multiobjective nonsmooth optimization |
| topic | multiobjective nonsmooth optimization cutting-plane model redistributed bundle method approximate calculation subgradient |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022710?viewType=HTML |
| work_keys_str_mv | AT jiatongli aredistributedcuttingplanebundletypealgorithmformultiobjectivenonsmoothoptimization AT jiatongli redistributedcuttingplanebundletypealgorithmformultiobjectivenonsmoothoptimization |