A Refined Proximal Algorithm for Nonconvex Multiobjective Optimization in Hilbert Spaces

Autor:	Bento, G. C., Neto, J. X. Cruz, Lopes, J. O., Mordukhovich, B. S., Filho, P. R. Silva
Rok vydání:	2024
Předmět:	Mathematics - Optimization and Control 90C26 90C29 49M05
Druh dokumentu:	Working Paper
Popis:	This paper is devoted to general nonconvex problems of multiobjective optimization in Hilbert spaces. Based on Mordukhovich's limiting subgradients, we define a new notion of Pareto critical points for such problems, establish necessary optimality conditions for them, and then employ these conditions to develop a refined version of the vectorial proximal point algorithm with providing its detailed convergence analysis. The obtained results largely extend those initiated by Bonnel, Iusem and Svaiter \cite{Bonnel2005} for convex vector optimization problems and by Bento et al. \cite{Bento2018} for nonconvex finite-dimensional problems in terms of Clarke's generalized gradients. Comment: 18 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2403.09922 Zobrazit plný text záznamu View this record from Arxiv