2024/03/14 by G. C. Bento, Bento, G. C., J. X. Cruz Neto +7 · 1 citation
Computer Science · Mathematics · #49M05 #90C26 #90C29 #Advanced Multi-Objective Optimization Algorithms #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2403.09922
openalex publication_date 2024/03/14 · openalex created_date 2024/03/19 · openalex updated_date 2026/07/28
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 \citeBonnel2005 for convex vector optimization problems and by Bento et al. \citeBento2018 for nonconvex finite-dimensional problems in terms of Clarke's generalized gradients.