| Under the appropriate assumptions in a topological vector space,some properties of Gerstewitz functional are discussed,including its separation for nonconvex sets.Moreover,the relationship between subset of minimal points and subset of minimal solutions of scalarization problem attained by Gerstewitz functional is established in this paper.Minewhile,a new kind of Gerstewitz functional with respect to a set is proposed as an extension of its general form,and some of its properties are discussed.Besides,the connection and difference between this Gerstewitz functional and other nonlinear scalarization functions are given in the end. |
