E-strongly Efficient Solution Of Set-valued Optimization Problem And Its Applications

The research of set-valued optimization has important theoretical value,and many scholars pay attention to efficiency of solutions.Because the classical efficiency of solutions can not reach a satisfactory level in terms of scalarization,based on the concept of improved set,we introduces the concept of E-strongly efficient point of set in locally convex space,and discusses the relationship between E-strongly efficient point and other properly efficient points.Secondly,under the assumption of near E-subconvexlikeness of set-valued maps,scalarization theorems,Kuhn-Tucker conditions,Lagrange multiplier theorems and E-strongly saddle point theorems of E-strongly efficient solution of set-valued optimization problems are established.The thesis is divided into four chapters,the main contents of this thesis are as follows.In chapter one,firstly,we analyze the background and significance of set-valued optimization.Secondly,we review some progresses of the efficiency of the solutions for set-valued optimization problems.Finally,we give the main contents of this thesis.In chapter two,firstly,we recall some basic concepts and properties,including convex set,cone,improved set,separation theorem of convex set and so on.These concepts and properties play an important role in the study of E-strongly efficient solutions for set-valued optimization problems.In chapter three,firstly,we recall the definitions of strongly efficient point and ?-strongly efficient point of a set.Secondly,Based on the concept of improved set,the E-strongly efficient point of a set is introduced in locally convex space.Finally,the relationship between E-strongly efficient point and other properly efficient points is discussed.In chapter four,we study the optimization condition of E-strongly efficient solutions.Under the assumption of near E-subconvexlikeness of set-valued maps,scalarization theorems,Kuhn-Tucker conditions and Lagrange multiplier theorems of E-strongly efficient solution of set-valued optimization problems are established.The definition of E-strongly saddle point is given,and the E-strongly saddle point theorems is established.