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The proximal point method for locally lipschitz functions in multiobjective optimization with application to the compromise problem

 

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Opened Access The proximal point method for locally lipschitz functions in multiobjective optimization with application to the compromise problem
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Author: Bento, Glaydston de Carvalho
Cruz Neto, João Xavier
López Acedo, Genaro
Soubeyran, Antoine
Oliveira Souza, Joao Carlos de
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2018
Published in: SIAM Journal on Optimization, 28 (2), 1104-1120.
Document type: Article
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, Iusem, and Svaiter [SIAM J. Optim., 15 (2005), pp. 953–970] is extended to locally Lipschitz functions in the finite dimensional multiobjective setting. To this end, a new (scalarization-free) 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 weak Pareto points of a multiobjective problem. As a consequence, this has allowed us to consider the method without any assumption of convexity over the constraint sets that determine the vectorial improvement steps. This is very important for applications; for example, to extend to a dynamic setting the famous compromise problem in management sciences and game theory.
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Format: PDF

URI: https://hdl.handle.net/11441/78385

DOI: 10.1137/16M107534X

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