A proximal subgradient algorithm for constrained multiobjective DC-type optimization
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912797781131264 |
|---|---|
| author | Van Tuyen, Nguyen Dao, Minh N. Van Nghi, Tran |
| author_facet | Van Tuyen, Nguyen Dao, Minh N. Van Nghi, Tran |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24717 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A proximal subgradient algorithm for constrained multiobjective DC-type optimization Van Tuyen, Nguyen Dao, Minh N. Van Nghi, Tran Optimization and Control 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. |
| title | A proximal subgradient algorithm for constrained multiobjective DC-type optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2512.24717 |