Proximal point method for a special class of nonconvex multiobjective optimization functions

TL;DR

This paper investigates the proximal point method for a specific class of nonconvex multiobjective functions, establishing conditions for convergence and critical point characterization.

Contribution

It introduces a convergence analysis for the proximal point method applied to certain nonconvex multiobjective problems, including conditions for full sequence convergence.

Findings

Generated sequences have accumulation points that are Pareto--Clarke critical points.

Under additional assumptions, the entire sequence converges.

The method is well defined for the studied class of functions.

Abstract

The proximal point method for a special class of nonconvex multiobjective functions is studied in this paper. We show that the method is well defined and that the accumulation points of any generated sequence, if any, are Pareto--Clarke critical points. Moreover, under additional assumptions, we show the full convergence of the generated sequence.