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The proximal point method for locally Lipschitz functions in multiobjective optimization

G.C. Bento(glaydston***at***ufg.br)
J.X. Cruz Neto(jxavier***at***ufpi.edu.br)
G. López(glopez***at***us.es)
A. Soubeyran(antoine.soubeyran***at***gmail.com)
J.C. Souza(joaocos.mat***at***ufpi.edu.br)

Abstract: This paper studies the constrained multiobjective optimization problem of finding Pareto critical points of vector-valued functions. The proximal point method considered by Bonnel et al. (SIAM J. Optim., 4 (2005), pp. 953-970) is extended to locally Lipschitz functions in the finite dimensional multiobjective setting. To this end, a new approach for convergence analysis of the method is proposed where the first-order optimality condition of the “scalarized” problem is replaced by a necessary condition for weakly Pareto points of a multiobjective problem.

Keywords: Proximal method, multiobjective optimization, locally Lipschitz function, Pareto critical point, compromise problem, variational rationality

Category 1: Other Topics (Multi-Criteria Optimization )

Category 2: Applications -- OR and Management Sciences

Citation: April, 2016.

Download: [PDF]

Entry Submitted: 06/21/2016
Entry Accepted: 06/21/2016
Entry Last Modified: 06/21/2016

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