Dubovitskii–Milyutin Approach in Set-Valued Optimization
George Isac, Akhtar Ali Khan · SIAM Journal on Control and Optimization · 2008
By exploring the ideas around the Dubovitskii–Milyutin approach, necessary optimality conditions are given for various optimality notions in set-valued optimization. These optimality conditions are given by using the contingent derivative and the generalized contingent epiderivative of the objective set-valued map and the set-valued maps defining the constraints. The notions of subgradients and scalarized subgradients for set-valued maps are proposed and used to state some regularity conditions.