Pareto Minimization Problem On Cone-Preinvex Mappings

Due to its profound significance in both application and theory, vector optimization problem has always been a hot topic in the research of nonlinear programming problems. It is well known that convex function plays an important role in the optimization theory. Although preinvex functions are not convex , they have some interesting properties. On the basis of the article of T. Weir and V.Jeyakumar about saddle point of Lagrange functions, optimality conditions and duality theorems given for both scalar-valued and vector-valued weak minimization problems involving cone-preinvex function, this paper discusses saddle point of Lagrange functions, optimality conditions, existence theorems of the solutions for generalized vector Variational inequality and duality problems in pareto minimization problems involving cone-preinvex function. Many relevent results are obtained.