A proximal subgradient algorithm for constrained multiobjective DC-type optimization

Nguyen Van Tuyen; Minh N. Dao; Tran Van Nghi

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arXiv · 2512.24717

A proximal subgradient algorithm for constrained multiobjective DC-type optimization

Nguyen Van Tuyen·Minh N. Dao·Tran Van Nghi

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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 a necessary optimality condition for these problems and then derive sufficient optimality conditions under some structural assumptions, 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 point. Numerical experiments on multi-sensor sparse recovery illustrate the effectiveness and computational advantages of the proposed algorithm.

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BibTeX RIS

Nguyen Van Tuyen, Minh N. Dao, Tran Van Nghi. 2025-12-31. A proximal subgradient algorithm for constrained multiobjective DC-type optimization. https://arxiv.org/abs/2512.24717

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