Optimality conditions in set-valued optimization using approximations as generalized derivatives

The set criterion is an appropriate defining approach regarding the solutions for the set-valued optimization problems. By using approximations as generalized derivatives of set-valued mappings, we establish necessary optimality conditions for a constrained set-valued optimization problem in the sense of set optimization in terms of asymptotical pointwise compact approximations. Sufficient optimality conditions are then obtained through first-order strong approximations of data set-valued mappings.