A Proximal Gradient Method with an Explicit Line search for Multiobjective Optimization
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914758111789056 |
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| author | Bello-Cruz, Yunier Melo, J. G. Prudente, L. F. Serra, R. V. G. |
| author_facet | Bello-Cruz, Yunier Melo, J. G. Prudente, L. F. Serra, R. V. G. |
| contents | We present a proximal gradient method for solving convex multiobjective optimization problems, where each objective function is the sum of two convex functions, with one assumed to be continuously differentiable. The algorithm incorporates a backtracking line search procedure that requires solving only one proximal subproblem per iteration, and is exclusively applied to the differentiable part of the objective functions. Under mild assumptions, we show that the sequence generated by the method convergences to a weakly Pareto optimal point of the problem. Additionally, we establish an iteration complexity bound by showing that the method finds an $\varepsilon$-approximate weakly Pareto point in at most ${\cal O}(1/\varepsilon)$ iterations. Numerical experiments illustrating the practical behavior of the method is presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10993 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Proximal Gradient Method with an Explicit Line search for Multiobjective Optimization Bello-Cruz, Yunier Melo, J. G. Prudente, L. F. Serra, R. V. G. Optimization and Control We present a proximal gradient method for solving convex multiobjective optimization problems, where each objective function is the sum of two convex functions, with one assumed to be continuously differentiable. The algorithm incorporates a backtracking line search procedure that requires solving only one proximal subproblem per iteration, and is exclusively applied to the differentiable part of the objective functions. Under mild assumptions, we show that the sequence generated by the method convergences to a weakly Pareto optimal point of the problem. Additionally, we establish an iteration complexity bound by showing that the method finds an $\varepsilon$-approximate weakly Pareto point in at most ${\cal O}(1/\varepsilon)$ iterations. Numerical experiments illustrating the practical behavior of the method is presented. |
| title | A Proximal Gradient Method with an Explicit Line search for Multiobjective Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2404.10993 |