A Refined Proximal Algorithm for Nonconvex Multiobjective Optimization in Hilbert Spaces
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929277979590656 |
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| author | Bento, G. C. Neto, J. X. Cruz Lopes, J. O. Mordukhovich, B. S. Filho, P. R. Silva |
| author_facet | Bento, G. C. Neto, J. X. Cruz Lopes, J. O. Mordukhovich, B. S. Filho, P. R. Silva |
| contents | This paper is devoted to general nonconvex problems of multiobjective optimization in Hilbert spaces. Based on Mordukhovich's limiting subgradients, we define a new notion of Pareto critical points for such problems, establish necessary optimality conditions for them, and then employ these conditions to develop a refined version of the vectorial proximal point algorithm with providing its detailed convergence analysis. The obtained results largely extend those initiated by Bonnel, Iusem and Svaiter \cite{Bonnel2005} for convex vector optimization problems and by Bento et al. \cite{Bento2018} for nonconvex finite-dimensional problems in terms of Clarke's generalized gradients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09922 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Refined Proximal Algorithm for Nonconvex Multiobjective Optimization in Hilbert Spaces Bento, G. C. Neto, J. X. Cruz Lopes, J. O. Mordukhovich, B. S. Filho, P. R. Silva Optimization and Control 90C26, 90C29, 49M05 This paper is devoted to general nonconvex problems of multiobjective optimization in Hilbert spaces. Based on Mordukhovich's limiting subgradients, we define a new notion of Pareto critical points for such problems, establish necessary optimality conditions for them, and then employ these conditions to develop a refined version of the vectorial proximal point algorithm with providing its detailed convergence analysis. The obtained results largely extend those initiated by Bonnel, Iusem and Svaiter \cite{Bonnel2005} for convex vector optimization problems and by Bento et al. \cite{Bento2018} for nonconvex finite-dimensional problems in terms of Clarke's generalized gradients. |
| title | A Refined Proximal Algorithm for Nonconvex Multiobjective Optimization in Hilbert Spaces |
| topic | Optimization and Control 90C26, 90C29, 49M05 |
| url | https://arxiv.org/abs/2403.09922 |