Scalarization of Henig properly efficient points in locally convex spaces
This paper investigates the scalarization of Henig proper efficiency in the framework of locally convex spaces without any convexity assumption on the feasible sets. By means of the properties of Gerstewitz's function, two versions of scalarizing Henig properly efficient points with respect to a base of the ordering cone are given. Then two further versions of scalarizing generalized Henig properly efficient points and Henig properly efficient points, respectively, are derived which only involve the ordering cone but do not refer to any special base. Since the scalarization results derived in this paper characterize (generalized) Henig properly efficient points by a single functional, any non-convex vector optimization problem defined by Henig proper efficiency can be converted into a scalar optimization problem. Finally, several conditions are derived which guarantee that every generalized Henig properly efficient point is also a Henig properly efficient point.
scientific article; zbMATH DE number 5823115