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

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.