Extended Pareto Optimality in Multiobjective Problem

This paper contains new developments on necessary conditions for minimal points of sets and their applications to deriving refined necessary optimality conditions in general models of set-valued optimization with geometric, functional, and operator constraints in finite and infinite dimensions. The results obtained address the new notions of extended Pareto optimality with preference relations generated by ordering sets satisfying the local asymptotic closedness property instead of that generated by convex and closed cones. In this way we unify and extend most of the known notions of efficiency/optimality in multiobjective models and establish optimality conditions that are new even in standard settings. Our approach is based on advanced tools of variational analysis and generalized differentiation