Cone Characterizations About Efficient Points And Efficient Solutions Of Vector Optimization Problems With Set-Valued Maps

In this thesis, we study the cone characterizations of efficient points (solutions) of the vector optimization problems in Hausdorff locally convex topological vector space. At first, we discuss the cone characterizations of efficient points (locally efficient points) when the nonempty set D satisfies (doesn't satisfy) the conditions of convexity. Secondly, for the efficient solutions and locally efficient solutions in vector optimization problems with set-valued maps, we give the cone characterizations that we find out the necessary optimality conditions of the optimal target value by the way of the feasible criterion set first; and then, we get the necessary optimality conditions of locally optimal solutions and locally weakly optimal solutions in the feasible set directly.