Artículo
The proximal point method for locally lipschitz functions in multiobjective optimization with application to the compromise problem
Autor/es | Bento, Glaydston de Carvalho
Cruz Neto, João Xavier López Acedo, Genaro Soubeyran, Antoine Oliveira Souza, Joao Carlos de |
Departamento | Universidad de Sevilla. Departamento de Análisis Matemático |
Fecha de publicación | 2018 |
Fecha de depósito | 2018-09-10 |
Publicado en |
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Resumen | 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 ... 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. |
Identificador del proyecto | 201210267000909 - 05/2012
458479/2014-4 471815/2012-8 312077/2014-9 88881.117595/2016-01 305462/2014-8 MTM2015-65242-C2-1-P ANR-16-CE03-0005 203360/2014-1 |
Cita | Bento, G.d.C., Cruz Neto, J.X., López Acedo, G., Soubeyran, A. y Oliveira Souza, J.C.d. (2018). The proximal point method for locally lipschitz functions in multiobjective optimization with application to the compromise problem. SIAM Journal on Optimization, 28 (2), 1104-1120. |
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