{"ID":2877752,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.20071","arxiv_id":"2508.20071","title":"A Partially Derivative-Free Proximal Method for Composite Multiobjective Optimization in the Hölder Setting","abstract":"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.","short_abstract":"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 compre...","url_abs":"https://arxiv.org/abs/2508.20071","url_pdf":"https://arxiv.org/pdf/2508.20071v2","authors":"[\"V. S. Amaral\",\"P. B. Assunção\",\"D. R. Souza\"]","published":"2025-08-27T17:34:28Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}