Incremental Delayed Subgradient Method for Decentralized Nonsmooth Convex–Concave Minimax Optimization
In this paper, we propose an incremental-type subgradient scheme for solving a nonsmooth convex–concave minimax optimization problem in the setting of Euclidean spaces. We investigate convergence results by deriving an upper bound for the absolute value of the difference between the function value o...
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MDPI AG
2025-02-01
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| Series: | Algorithms |
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| Online Access: | https://www.mdpi.com/1999-4893/18/3/126 |
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| author | Thipagon Feesantia Tipsuda Arunrat Nimit Nimana |
| author_facet | Thipagon Feesantia Tipsuda Arunrat Nimit Nimana |
| author_sort | Thipagon Feesantia |
| collection | DOAJ |
| description | In this paper, we propose an incremental-type subgradient scheme for solving a nonsmooth convex–concave minimax optimization problem in the setting of Euclidean spaces. We investigate convergence results by deriving an upper bound for the absolute value of the difference between the function value of the averaged iterates and the saddle value, provided that the step size is a constant. By assuming that the step-size sequence is diminishing, we prove the convergences of both the averaged sequence of function values and the sequence of function values of averaged iterates to the saddle value. Finally, we also show some numerical examples for illustrating the obtained theoretical result. |
| format | Article |
| id | doaj-art-88d548c931e14b9eb9cd72bb6a989be6 |
| institution | Kabale University |
| issn | 1999-4893 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj-art-88d548c931e14b9eb9cd72bb6a989be62025-08-20T03:43:50ZengMDPI AGAlgorithms1999-48932025-02-0118312610.3390/a18030126Incremental Delayed Subgradient Method for Decentralized Nonsmooth Convex–Concave Minimax OptimizationThipagon Feesantia0Tipsuda Arunrat1Nimit Nimana2Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandDepartment of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandDepartment of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandIn this paper, we propose an incremental-type subgradient scheme for solving a nonsmooth convex–concave minimax optimization problem in the setting of Euclidean spaces. We investigate convergence results by deriving an upper bound for the absolute value of the difference between the function value of the averaged iterates and the saddle value, provided that the step size is a constant. By assuming that the step-size sequence is diminishing, we prove the convergences of both the averaged sequence of function values and the sequence of function values of averaged iterates to the saddle value. Finally, we also show some numerical examples for illustrating the obtained theoretical result.https://www.mdpi.com/1999-4893/18/3/126delayincremental methodminimax problemsaddle pointsubgradient method |
| spellingShingle | Thipagon Feesantia Tipsuda Arunrat Nimit Nimana Incremental Delayed Subgradient Method for Decentralized Nonsmooth Convex–Concave Minimax Optimization Algorithms delay incremental method minimax problem saddle point subgradient method |
| title | Incremental Delayed Subgradient Method for Decentralized Nonsmooth Convex–Concave Minimax Optimization |
| title_full | Incremental Delayed Subgradient Method for Decentralized Nonsmooth Convex–Concave Minimax Optimization |
| title_fullStr | Incremental Delayed Subgradient Method for Decentralized Nonsmooth Convex–Concave Minimax Optimization |
| title_full_unstemmed | Incremental Delayed Subgradient Method for Decentralized Nonsmooth Convex–Concave Minimax Optimization |
| title_short | Incremental Delayed Subgradient Method for Decentralized Nonsmooth Convex–Concave Minimax Optimization |
| title_sort | incremental delayed subgradient method for decentralized nonsmooth convex concave minimax optimization |
| topic | delay incremental method minimax problem saddle point subgradient method |
| url | https://www.mdpi.com/1999-4893/18/3/126 |
| work_keys_str_mv | AT thipagonfeesantia incrementaldelayedsubgradientmethodfordecentralizednonsmoothconvexconcaveminimaxoptimization AT tipsudaarunrat incrementaldelayedsubgradientmethodfordecentralizednonsmoothconvexconcaveminimaxoptimization AT nimitnimana incrementaldelayedsubgradientmethodfordecentralizednonsmoothconvexconcaveminimaxoptimization |