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

Gadhi Nazih Abderrazzak, Ichatouhane Aissam

Control and Cybernetics

2022

Vol. 51, No. 4

425--444

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.