| In the framework of real linear spaces,we introduce three kinds of Henig proper efficient points.By using the Hahn-Banach separation theorem on convex sets in real linear spaces,we establish the scalarization theorems of the three kinds of Henig proper efficient points respectively.From this,we obtain the scalarizations on Henig proper efficient solutions of vector optimization problems involving nearly cone-subconvexlike vector-vaiued maps and set-valued maps respectively.Moreover,by using the Hahn-Banach separation theorem on product spaces,we give Lagrange multiplier theorems on Henig proper efficient solutions of vector optimization problems involving vector-valued maps and set-valued set maps with constraint.Many known results have been extended to real linear spaces.A new concept of Henig proper efficiency,only involving relatively algebric interior,is introduced and its scalarization is obtained. |
