An Infeasible Incremental Bundle Method for Nonsmooth Optimization Problem Based on CVaR Portfolio
For CVaR (conditional value-at-risk) portfolio nonsmooth optimization problem, we propose an infeasible incremental bundle method on the basis of the improvement function and the main idea of incremental method for solving convex finite min-max problems. The presented algorithm only employs the info...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/6640781 |
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| author | Jia-Tong Li Jie Shen Na Xu |
| author_facet | Jia-Tong Li Jie Shen Na Xu |
| author_sort | Jia-Tong Li |
| collection | DOAJ |
| description | For CVaR (conditional value-at-risk) portfolio nonsmooth optimization problem, we propose an infeasible incremental bundle method on the basis of the improvement function and the main idea of incremental method for solving convex finite min-max problems. The presented algorithm only employs the information of the objective function and one component function of constraint functions to form the approximate model for improvement function. By introducing the aggregate technique, we keep the information of previous iterate points that may be deleted from bundle to overcome the difficulty of numerical computation and storage. Our algorithm does not enforce the feasibility of iterate points and the monotonicity of objective function, and the global convergence of the algorithm is established under mild conditions. Compared with the available results, our method loosens the requirements of computing the whole constraint function, which makes the algorithm easier to implement. |
| format | Article |
| id | doaj-art-a4d5686442804c80bbc5e00cd321abc2 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-a4d5686442804c80bbc5e00cd321abc22025-02-03T01:28:43ZengWileyComplexity1076-27871099-05262021-01-01202110.1155/2021/66407816640781An Infeasible Incremental Bundle Method for Nonsmooth Optimization Problem Based on CVaR PortfolioJia-Tong Li0Jie Shen1Na Xu2College of Science, Northeast Forestry University, Harbin 150040, ChinaSchool of Mathematics, Liaoning Normal University, Dalian 116029, ChinaSchool of Mathematics, Liaoning Normal University, Dalian 116029, ChinaFor CVaR (conditional value-at-risk) portfolio nonsmooth optimization problem, we propose an infeasible incremental bundle method on the basis of the improvement function and the main idea of incremental method for solving convex finite min-max problems. The presented algorithm only employs the information of the objective function and one component function of constraint functions to form the approximate model for improvement function. By introducing the aggregate technique, we keep the information of previous iterate points that may be deleted from bundle to overcome the difficulty of numerical computation and storage. Our algorithm does not enforce the feasibility of iterate points and the monotonicity of objective function, and the global convergence of the algorithm is established under mild conditions. Compared with the available results, our method loosens the requirements of computing the whole constraint function, which makes the algorithm easier to implement.http://dx.doi.org/10.1155/2021/6640781 |
| spellingShingle | Jia-Tong Li Jie Shen Na Xu An Infeasible Incremental Bundle Method for Nonsmooth Optimization Problem Based on CVaR Portfolio Complexity |
| title | An Infeasible Incremental Bundle Method for Nonsmooth Optimization Problem Based on CVaR Portfolio |
| title_full | An Infeasible Incremental Bundle Method for Nonsmooth Optimization Problem Based on CVaR Portfolio |
| title_fullStr | An Infeasible Incremental Bundle Method for Nonsmooth Optimization Problem Based on CVaR Portfolio |
| title_full_unstemmed | An Infeasible Incremental Bundle Method for Nonsmooth Optimization Problem Based on CVaR Portfolio |
| title_short | An Infeasible Incremental Bundle Method for Nonsmooth Optimization Problem Based on CVaR Portfolio |
| title_sort | infeasible incremental bundle method for nonsmooth optimization problem based on cvar portfolio |
| url | http://dx.doi.org/10.1155/2021/6640781 |
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