Optimality conditions for vector optimization problems with generalized convexity in real linear spaces

In this paper we consider mainly vector optimization problems under generalized cone-convexlikeness and generalized cone-subconvexlikeness in real linear spaces having or not topology. We establish the adapted definitions to wide frame of real linear spaces, and we show the characterizations for several concepts of generalized convexity and the relationships among them. From separation theorems, some characterizations of efficiency and weak efficiency are given in terms of scalarization. A new extension of Gordan-form alternative theorem is given here, and derived from it, we obtain optimality conditions by means of linear operators rules and saddle point criterions.