VECTORIZATION IN NONCONVEX SET OPTIMIZATION

A new vectorization approach is presented for nonconvex set optimization problems with the set less order relation. This technique uses certain approximation problems with suitable parametric norms. The convexity of the sets is not required but one needs a strict lower and upper bound for all occuring sets. Karush-Kuhn-Tucker conditions are derived as necessary optimality conditions for set optimization problems in finite dimensional Euclidean spaces with the natural order cone. A multiplier-free necessary optimality condition is given as well. ©2022 Journal of Applied and Numerical Optimization