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A Scalarization Proximal Point Method for Quasiconvex Multiobjective Minimization

H.C.F. Apolinário (hellenato***at***cos.ufrj.br)
E.A. Papa Quiroz (erikpapa***at***gmail.com)
P. R. Oliveira (poliveir***at***cos.ufrj.br)

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).

Keywords: Multiobjective minimization, Clarke subdifferential, quasiconvex functions, proximal point methods, Fejer convergence, Pareto-Clarke critical point. e

Category 1: Other Topics (Multi-Criteria Optimization )

Category 2: Convex and Nonsmooth Optimization (Generalized Convexity/Monoticity )

Category 3: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Federal University of Rio de Janeiro, Computing and Systems Engineering Department,21945-970, Rio de Janeiro, Brazil,March/2014

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Entry Submitted: 03/01/2014
Entry Accepted: 03/01/2014
Entry Last Modified: 07/24/2014

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