Weak Sharp Minima in Set-Valued Optimization Problems

Abstract

We introduce the notion of a weak ψ-sharp minimizer for set-valued optimization problems. We present some sufficient and necessary conditions that a pair point is a weak ψ-sharp minimizer through the outer limit of set-valued map and develop the characterization of the weak ψ-sharp minimizer in terms of a generalized nonlinear scalarization function. These results extend the corresponding ones in Studniarski (2007).