Study On Characterizations Of S-Benson Proper Effcient Solutions In Vector Optimization

Study on approximate solutions of vector optimization problems is an important research aspect in the field of theory and methods of vector optimization problems. It is meaningful to study some characterizations of the solutions of vector optimization problems by means of improvement sets or assumption B in a unified framework. In this paper, we mainly consider S-Benson proper e?cient solutions via assumption B and the ideas of the classical Benson proper e?cient solutions for vector optimization problems,and establish the linear scalarization theorem, lagrange multiplier theorems and some nonlinear scalarization characterizations of S-Benson proper e?cient solutions for vector optimization problems.Chapter 1 gives some main research advancements about characterizations of the several kinds of solutions for vector optimization problems and some basic concepts and tools in vector optimization problems.Chapter 2 gives some topological properties of improvement sets. These properties improve and generalize some known and classical results for the case of convexity.Chapter 3 firstly propose the concept of a kind of new generalized convexity named as S-subconvexlikeness and establish the corresponding alternative theorem of S-subconvexlikeness. S-subconvexlikeness includes the classical Esubconvexlikeness via improvement sets and cone-subconvexlikeness as its special cases. Furthermore, under the S-subconvexlikeness, we establish the linear scalarization theorem, lagrange multiplier theorem of S-Benson proper e?cient solutions for set-valued vector optimization problems. These results generalize those corresponding results in the sense of E-Benson proper e?cient solutions.Chapter 4 consider a class of vector-valued optimization problems and gives some nonlinear scalarization results of S-Benson proper e?cient solutions by means of a kind of classical nonlinear scalarization functional and the corresponding nonconvex separation theorem.