Study On Characterization Of Approximate Proper Efficiency In Vector Optimization Problems With Set-Valued Maps

It is well known that approximate proper e?ciency have been playing an important role in studing the theory and methods of optimization. In particular, it’s meaningful to study the scalarization theorems and the Kuhn-Tucker optimality conditions of approximate proper e?ciency. This paper, the set-valued optimization problem with constraints is considered in the sense of ε-super e?ciency and(C,)-proper e?ciency. A new scalarization result of ε-supper e?cient solutions is obtained. Moreover, the Kuhn-Tucker optimality conditions of ε-supper e?cient solutions and(C,)-proper e?cient solutions are derived. Also, a kind of unconstrained program equivalent to vector optimization problems is established in the sense of ε-super e?ciency and(C,)-proper e?ciency.In chapter 2, some characterizations of ε-super e?ciency is given. Moreover, a necessary condition of ε-super e?cient point is obtained in locally convex topological vector space and a su?cient condition of ε-super e?cient point is derived in locally convex locally bounded topological vector spaces. Finally, a new scalarization result of ε-super e?ciency is established in locally convex locally bounded topological vector spaces.In chapter 3, the Kuhn-Tucker optimality conditions are established in the sense of ε-super e?cient solutions. Under the assumption of nearly cone-subconvexlikeness, a Kuhn-Tucker optimality necessary condition of ε-super e?cient solutions is derived, and a su?cient condition of ε-super e?cient solutions is also obtained. These results are more generalization than the results in sense of ic-cone-convelikeness. Finally, a kind of unconstrained program equivalent to vector optimization problems is established.In chapter 4, Kuhn-Tucker optimality conditions are established in the sense of(C,)-proper e?cient solutions. Under the assumption of nearly(C,)-subconvexlikeness, a Kuhn-Tucker optimality necessary condition of(C,)- proper e?cient solutions is derived and a su?cient condition of(C,)-proper e?cient solutions is also obtained. Finally, a kind of unconstrained program equivalent to vector optimization problems is established.