Study On Stability And Connectedness Of Set Optimization Problems

In this thesis,we mainly study the stability of the solution and the connectedness of the solution set of set optimization problems.The bilevel set optimization problem model is established by introducing the variable partial order structure,and the stability results of the solution mapping of the bilevel set optimization problem under semi-continuity are obtained.In addition,under the assumption of strictly coneconvexlikeness,the arc connectivity and stability of the solution set of the set optimization problem are discussed by using the numerical method and a new density result.These results obtained in this paper extend and develop some recent works in the literature.The full text is divided into four chapters as follows:In the first chapter,we mainly introduce the generation and development of set optimization problems.Combined with the development status of related research on set optimization problems,the content of this paper is proposed.The framework of this paper is briefly described.Finally,the concepts,lemmas and known conclusions needed in this paper are given.In the second chapter,the variable partial order structure is firstly introduced,and then the variable order relationship of the set is given,and the bilevel set optimization problem model is established by combining the variable partial order structure.In addition,using the infinite upper continuity of the variable control structure and the finite cover theorem of the compact set,the sufficient conditions for the upper semicontinuity and Hausdorff upper semicontinuity of the solution mapping of the bilevel set optimization problem are obtained under two different variable order structures.In the third chapter,under the strict cone-convexlike assumption,the arc connectivity of the six effective solutions of the set optimization problem is established.Furthermore,by using the numerical method and a new density result,we give the numerical characterization of the lower semi-continuity of the six effective solution mappings of the parametric set optimization problem.Finally,by using the density results,the upper semicontinuity of the weakly efficient solution mapping of the parametric set optimization problem is obtained,and the global efficient solution mapping of the parametric set optimization problem and the Hausdorff upper semicontinuity of the efficient solution mapping are also obtained.In the last chapter,we summarize the article and put forward the prospect.