{"ID":2823671,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.24717","arxiv_id":"2512.24717","title":"A proximal subgradient algorithm for constrained multiobjective DC-type optimization","abstract":"In this paper, we consider a class of constrained multiobjective optimization problems, where each objective function can be expressed by adding a possibly nonsmooth nonconvex function and a differentiable function with Lipschitz continuous gradient, then subtracting a weakly convex function. This encompasses multiobjective optimization problems involving difference-of-convex (DC) functions, which are prevalent in various applications due to their ability to model nonconvex problems. We first establish necessary and sufficient optimality conditions for these problems, providing a theoretical foundation for algorithm development. Building on these conditions, we propose a proximal subgradient algorithm tailored to the structure of the objectives. Under mild assumptions, the sequence generated by the proposed algorithm is bounded and each of its cluster points is a stationary solution.","short_abstract":"In this paper, we consider a class of constrained multiobjective optimization problems, where each objective function can be expressed by adding a possibly nonsmooth nonconvex function and a differentiable function with Lipschitz continuous gradient, then subtracting a weakly convex function. This encompasses multiobje...","url_abs":"https://arxiv.org/abs/2512.24717","url_pdf":"https://arxiv.org/pdf/2512.24717v1","authors":"[\"Nguyen Van Tuyen\",\"Minh N. Dao\",\"Tran Van Nghi\"]","published":"2025-12-31T08:31:49Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}