Duality Theorems of Multiobjective Programming for a Class of Generalized Convex Functions

Many important achievement of multiobjective programming are all based on convex programming. How to extend and deepen them, one vital aspect is extend the convexity functions which are refered in various sense to more general convexity functions. In this paper, a class of generalized convexity fuctions: (F, rho )-invariant convex function, (F, rho)- invariant quasiconvex function, (F, rho )-invariant pseudoconvex function and (F, rho )-strictly invariant pseudoconvex function are defined. On the basis of definitions, we have constructed general duality models (VD); discussed duality property of (VP) and (VD); proved weakly duality theorem, direct duality theorem and converse duality theorem. The functions of a class of generalized convexity are extension of the several different generalized convexity functions presented in the references (X.M Yiang, 1991), (Y.Z. Li, 1993), (M.A. Hanson et al., 1982), (C.Y. Lin et al., 1992) and (M.A. Hanson, 1981). The results of this paper can be thought of as improved extended and generalized of the main results of the references (X.M Yiang, 1991), (Y.Z,. Li, 1993), (M.A. Hanson et al., 1982), (C.Y. Lin et al., 1992) (M.A. Hanson, 1981), (C.Y. Lin, 1987,1998,1981,1985), and (D.G. Mahajan et al., 1997).