Study On Characterizations Of Proper Effcient Solutions Via Recession Cone In Vector Optimization

Research on characterizations of the solution of vector optimization problems is an mportant research scope in vector optimization. Improvement sets is a kind of very mportant tool to deal with vector optimization problems in a unified framework. Study on characterizations of weakly efficient solutions via improvement sets, efficient solutions via mprovement sets and properly efficient solutions via improvement sets has been paid more ttentions in vector optimization. In this paper, we mainly study some characterizations of properly efficient solutions via Recession Cone defined by improvement sets and recession eone, including some saddle point theorems, some duality results and some nonlinear scalarization characterizations.Chapter 1 present some research background of vector optimization problems, some advancements on characterizations of the solutions and some basic concepts and tools in ector optimization.Chapter 2 mainly establish some saddle point theorems and some duality results of properly efficient solutions via Recession Cone of vector optimization problems with set-valued maps in a general real local convex Hausdorff topological linear space by making use of the E-subconvexlikeness and the corresponding alternative theorem. These main esults improve and generalize the corresponding results in the sense of E-Benson properly efficient solutions.Chapter 3 gives some nonlinear scalarization characterizations of E-Benson properly efficient solutions via Recession Cone of vector-valued optimization problems by mak-ng use of two kind of classical nonlinear scalarization functions and the corresponding...