A Scalarization Proximal Point Method for Quasiconvex Multiobjective Minimization

Abstract

In this paper we propose a scalarization proximal point method to solve multiobjective unconstrained minimization problems with locally Lipschitz and quasiconvex vector functions. We prove, under natural assumptions, that the sequence generated by the method is well defined and converges globally to a Pareto-Clarke critical point. Our method may be seen as an extension, for the non convex case, of the inexact proximal method for multiobjective convex minimization problems studied by Bonnel et al. (SIAM Journal on Optimization 15, 4, 953-970, 2005).

Several applications in diverse Science and Engineering areas are motivation to work with nonconvex multiobjective functions and proximal point methods. In particular the class of quasiconvex minimization problems has been receiving attention from many researches due to the broad range of applications in location theory, control theory and specially in economic theory