A Partially Derivative-Free Proximal Method for Composite Multiobjective Optimization in the Hölder Setting
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912853863170048 |
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| author | Amaral, V. S. Assunção, P. B. Souza, D. R. |
| author_facet | Amaral, V. S. Assunção, P. B. Souza, D. R. |
| contents | This paper presents an algorithm for solving multiobjective optimization problems involving composite functions, where we minimize a quadratic model that approximates $F(x) - F(x^k)$ and that can be derivative-free. We establish theoretical assumptions about the component functions of the composition and provide comprehensive convergence and complexity analysis. Specifically, we prove that the proposed method converges to a weakly $\varepsilon$-approximate Pareto point in at most $\mathcal{O}\left(\varepsilon^{-\frac{β+1}β}\right)$ iterations, where $β$ denotes the Hölder exponent of the gradient. The algorithm incorporates gradient approximations and a scaling matrix $B_k$ to achieve an optimal balance between computational accuracy and efficiency. Numerical experiments on a collection of benchmark problems are presented, illustrating the practical behavior of the proposed approach and its competitiveness with existing composite algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_20071 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Partially Derivative-Free Proximal Method for Composite Multiobjective Optimization in the Hölder Setting Amaral, V. S. Assunção, P. B. Souza, D. R. Optimization and Control This paper presents an algorithm for solving multiobjective optimization problems involving composite functions, where we minimize a quadratic model that approximates $F(x) - F(x^k)$ and that can be derivative-free. We establish theoretical assumptions about the component functions of the composition and provide comprehensive convergence and complexity analysis. Specifically, we prove that the proposed method converges to a weakly $\varepsilon$-approximate Pareto point in at most $\mathcal{O}\left(\varepsilon^{-\frac{β+1}β}\right)$ iterations, where $β$ denotes the Hölder exponent of the gradient. The algorithm incorporates gradient approximations and a scaling matrix $B_k$ to achieve an optimal balance between computational accuracy and efficiency. Numerical experiments on a collection of benchmark problems are presented, illustrating the practical behavior of the proposed approach and its competitiveness with existing composite algorithms. |
| title | A Partially Derivative-Free Proximal Method for Composite Multiobjective Optimization in the Hölder Setting |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2508.20071 |