Conjugate gradient methods without line search for multiobjective optimization
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913542394871808 |
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| author | Chen, Wang Zhao, Yong Tang, Liping Yang, Xinmin |
| author_facet | Chen, Wang Zhao, Yong Tang, Liping Yang, Xinmin |
| contents | This paper addresses unconstrained multiobjective optimization problems where two or more continuously differentiable functions have to be minimized. We delve into the conjugate gradient methods proposed by Lucambio Pérez and Prudente (SIAM J Optim, 28(3): 2690--2720, 2018) for such problems. Instead of the Wolfe-type line search procedure used in their work, we employ a fixed stepsize formula (or no-line-search scheme), which can mitigate the pressure of choosing stepsize caused by multiple inequalities and avoid the computational cost associated with function evaluations in specific applications. The no-line-search scheme is utilized to derive the condition of Zoutendijk's type. Global convergence encompasses the vector extensions of Fletcher--Reeves, conjugate descent, Dai--Yuan, Polak--Ribière--Polyak and Hestenes--Stiefel parameters, subject to certain mild assumptions. Additionally, numerical experiments are conducted to demonstrate the practical performance of the proposed stepsize rule, and comparative analyses are made with the multiobjective steepest descent methods using the Armijo line search and the multiobjective conjugate gradient methods using the Wolfe-type line search. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_02461 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Conjugate gradient methods without line search for multiobjective optimization Chen, Wang Zhao, Yong Tang, Liping Yang, Xinmin Optimization and Control This paper addresses unconstrained multiobjective optimization problems where two or more continuously differentiable functions have to be minimized. We delve into the conjugate gradient methods proposed by Lucambio Pérez and Prudente (SIAM J Optim, 28(3): 2690--2720, 2018) for such problems. Instead of the Wolfe-type line search procedure used in their work, we employ a fixed stepsize formula (or no-line-search scheme), which can mitigate the pressure of choosing stepsize caused by multiple inequalities and avoid the computational cost associated with function evaluations in specific applications. The no-line-search scheme is utilized to derive the condition of Zoutendijk's type. Global convergence encompasses the vector extensions of Fletcher--Reeves, conjugate descent, Dai--Yuan, Polak--Ribière--Polyak and Hestenes--Stiefel parameters, subject to certain mild assumptions. Additionally, numerical experiments are conducted to demonstrate the practical performance of the proposed stepsize rule, and comparative analyses are made with the multiobjective steepest descent methods using the Armijo line search and the multiobjective conjugate gradient methods using the Wolfe-type line search. |
| title | Conjugate gradient methods without line search for multiobjective optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2312.02461 |