Weak sharp minima in set-valued optimization problems (Q1938341)

Summary: We introduce the notion of a weak \(\psi \)-sharp minimizer for set-valued optimization problems. We present some sufficient and necessary conditions that a pair point is a weak \(\psi \)-sharp minimizer through the outer limit of a set-valued map and develop the characterization of the weak \(\psi \)-sharp minimizer in terms of a generalized nonlinear scalarization function. These results extend the corresponding ones by \textit{M. Studniarski} [Control Cybern. 36, No. 4, 925--937 (2007; Zbl 1227.90036)].