Studies On Well-posedness And Scalarization Of Set Optimization Problem In A Variable Ordering Framework

Based on the variable order relationship of sets,this dissertation mainly discusses the well-posedness of set optimization problems and the scalarization results of their solutions.Under the condition that the objective map has appropriate semi continuity,the sufficient and necessary conditions for the generalized fitness for variable partial order structures in set optimization problems are obtained;Furthermore,a nonlinear scalar function under set order relation is introduced,and the important properties of the function are discussed in depth.Finally,the scalar results of the minimal solution of the variable set optimization problem are obtained using the obtained properties.The main results obtained in this paper generalize and develop recent relevant research results in this field.The thesis consists of four chapters as follows:In chapter 1,this dissertation introduces the historical background and developpment status of set optimization problems,and then proposes the main research content and significance of this article.In the last part of this chapter,the definitions,lemmas,and known conclusions used in this paper are given.In chapter 2,in the framework of variable order,we mainly study the generalized well posedness of set optimization problems.Firstly,by introducing three different variable order relationships about sets through the variable partial order structure,the corresponding generalized well-posedness concept for variable set optimization problems is proposed.Secondly,in order to facilitate the discussion,the concepts of approximate solution sets and mappings for variable set optimization problems are also proposed,and their properties are analyzed in depth.Finally,the existence results of weak minimum solutions and the scalarization results of minimum solutions for set optimization problems under variable order relationships were obtained.In chapter 4,we summarizes the main research contents of this paper and put forward the future research ideas and prospects.