Applied Math Seminar Announcement

Set-valued optimization is a relatively new branch of optimization in which one deals with minimization/maximization of set-valued maps. The notion of a minimizer/maximizer is defined by using positive ordering cones.

This seminar is devoted to the optimality conditions in set-valued optimization. By exploring the ideas around the so-called Dubovitskii-Milyutin approach, necessary optimality conditions are given for various optimality notions in set-valued optimization. These optimality conditions are given by employing 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 employed to state some regularity conditions.