Nonconvex separation theorems and application

ABSTRACTIn this study, structures for separation of two sets which are not to be necassary convex ineuclidean space are presented. These structures depend on combining different approaches forthe sets which cannot be separated by hyperplanes. Because of that, nonnegative cones areselected and built on well defined function.First of all, convex sets are taken into consideration and hyperplanes separation of two convexsets and hyperplanes presented by supporting with hyperplanes at boundary point. Then,separation of not necassarily convex sets that are provided by well defined function. Finally,an application by using the scalarization result in nonconvex vector optimization is presented.Key words: convex sets, nonconvex sets, hyperplane separation of sets, efficient point,weakly efficient pointvii