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Lagrangian multipliers for generalized affine and generalized convex vector optimization problems of set-valued maps

Zeng Renying

Journal of Applied Analysis

2021

Vol. 27, nr 2

163--173

In this paper, we introduce some definitions of generalized affine set-valued maps: affinelike, preaffinelike, nearaffinelike, and prenearaffinelike maps. We present examples to explain that our definitions of generalized affine maps are different from each other. We derive a theorem of alternative of Farkas-Minkowski type, discuss Lagrangian multipliers for constrained set-valued optimization problems, and obtain some optimality conditions for weakly efficient solutions.