Weak sharp minima in set-valued optimization problems. (English) Zbl 1263.90085

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 M. Studniarski [Control Cybern. 36, No. 4, 925–937 (2007; Zbl 1227.90036)].


90C29 Multi-objective and goal programming
90C46 Optimality conditions and duality in mathematical programming


Zbl 1227.90036
Full Text: DOI


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