2018-09-102018-09-102018Bento, 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), 1104-1120.1052-62341095-7189https://hdl.handle.net/11441/78385This 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.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Proximal point methodMultiobjective optimizationLocally Lipschitz functionPareto critical pointCompromise problemVariational rationalityinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.1137/16M107534X