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Relative Pareto Minimizers To Multiobjective Problems: Existence And Optimality Conditions, Truong Q. Bao, Boris S. Mordukhovich

Mathematics Research Reports

In this paper we introduce and study enhanced notions of relative Pareto minimizers to constrained multiobjective problems that are defined via several kinds of relative interiors of ordering cones and occupy intermediate positions between the classical notions of Pareto and weak Pareto efficiency/minimality. Using advanced tools of variational analysis and generalized differentiation, we establish the existence of relative Pareto minimizers to general multiobjective problems under a refined version of the subdifferential Palais-Smale condition for set-valued mappings with values in partially ordered spaces and then derive necessary optimality conditions for these minimizers (as well as for conventional efficient and weak efficient …