Berge Semicontinuity And Painlevé-Kuratowski Convergence Of Set-valued Optimization Problems

It is well known that the stability analysis of set-valued optimization problems is one of the hotspots in the optimization theory and application.The research results can not only enrich the optimization theory,but also provide theoretical support for algorithm.It can be applied to economic management,engineering design,traffic control and so on.Therefore,the stability analysis of set-valued optimization problems has strong significance and value.This thesis devoted to investigate the Berge semicontinuity and the Painlevé-Kuratowski convergence for set-valued optimization problems.The thesis mainly studies three aspects as follows:1.Stability for semi-infinite vector optimization problems via generalized order setsWhen the order set is not necessary a convex set or cone,by using properties of recession cone and weaker assumptions,we discuss upper Painlevé-Kuratowski convergence of efficient solution sets,Benson proper efficient solution sets,Borwein proper efficient solution sets and Henig proper efficient solution sets for semi-infinite vector optimization problems(SIVO).Then,we use examples to illustrate the feasibility of the theoretical results.2.Painlevé-Kuratowski convergence of minimal solutions for set-valued optimization problems via improvement setsWhen the order set is an improvement set,which is not necessary a cone,by using a new convergence concept for set-valued mapping,we discuss the PainlevéKuratowski convergences of - and weak --minimal solutions to set-valued optimization problems under mild conditions.Finally,we use examples to verify the feasibility of the theoretical results.3.On the solution stability for parametric set optimization problems under improvement sets without convexityWhen the order set is an improvement set,which is not necessary a cone,without any convexity assumption of objective functions,we discuss the sufficient conditions for Berge upper and lower semicontinuity of(weak)minimal solution mappings for parametric set optimization problems.Finally,two shortcomings in the corresponding literature are pointed out,and some examples are given to illustrate obtained results.