Study On Characterizations Of E-Benson Proper Efficient Solutions In Real Ordered Linear Spaces

Study on characterizations of the solutions of vector optimization problems is an important research aspect for the theory and methods of vector optimization problems.So far as, there are a lot of important research results on characterizations of the solutions in a general real topological linear space. When the image space of a vector optimization problem is a general real linear space, i.e., there is no topological structure, it also becomes an important research issue how to study the characterizations of the di?erent kinds of solutions by means of some tools such as algebraic interior and vector closure. In this paper, we mainly give some characterizations of improvement sets and E-Benson proper e?cient solutions by using algebraic interior and vector closure in a general real linear space and discuss some special cases.Chapter 1 gives some main research background of vector optimization problems and some main advancements on characterizations of the di?erent kinds of solutions for vector optimization problems.Chapter 2 gives some topological characterizations. These results improve and generalize some known results for convex set.Chapter 3 proposes the concept of E-Benson proper e?cient solutions of vector optimization problems by means of algebraic interior and vector closure and the ideas of E-Benson proper e?cient solutions in a general real linear space. Furthermore, under the assumption of the nearly E-subconvexlikeness, some scalarization theorem, lagrange multiplier theorem, saddle point theorem and duality results of E-Benson proper e?cient solutions are established for set-valued vector optimization problems.Chapter 4 discuss some special cases of the main results obtained in chapter 3. Scalarization theorem, lagrange multiplier theorem, saddle point theorem and duality results of(C,)-proper e?cient solutions are given for set-valued vector optimization problems.