Research On Connectedness Of The Set Of Effective Points For Parameric Set-value Vector Optimization Problem

The correlation properties of effective point sets in set-valued vector optimization problems of a subject worthy of discussion.Among them,connectedness plays an irreplaceable role,which can make the elements in the set move continuously,which also provides the possibility for the sustainable movement of the effective point set in the optimization problem of set value vector.The key point of this paper is to study the connectedness of Henig effective point set,strongly effective point set and globally valid point set in the case of object set-valued mapping with parameters in locally convex Hausdorff topological vector space.The main contents are as follows:The first chapter is the introduction,which focuses on the research background and development significance of the effectiveness of vector optimization problem and its solution set,summarizes the research results at home and abroad,and points out the innovation of this paper.The second chapter,introduce the basic theoretical knowledge of study the correlation properties of effective point sets in the set-valued vector optimization problems,such as topological vector space,set-valued mapping and its continuity,correlation properties of cones,convex set isolation theorem,etc.The third chapter mainly proves the connectedness of Henig efficient point sets for parameters set-valued vector optimization problems,this chapter introduces the concept of Henig efficient point,and gives the concept of parameters Henig effective point set,and under the condition that the object set with parameters set-valued mapped is Cone-arc connection,and the parameters in the case of change,obtained the set-valued vector optimization problems the theorem of the Henig efficient point sets connectedness.The fourth chapter mainly proves the connectedness of strong effective point set in the parameters set-valued vector optimization problems.This chapter introduces the concepts of strong effective point set in the parameters set-valued vector optimization problems,and gives the concept of strong effective point set with parameters.Under the condition that the parameter is change and the target set-valued mapping with parameter is Cone-arc connection,the connectedness theorem of strong effective point set in the parameters set-valued vector optimization problems is obtained.The fifth chapter mainly proves the connectedness of global really efficient point set in the parameters set-valued vector optimization problems,this chapter introduces the related concepts of global really efficient point,and contain the parameter is given the concept of global really efficient point set,and under the condition that the object set with parameters set-valued mapped is Cone-arc connection,and the parameters in the case of change,the connectedness theorem of global really efficient point sets in the parameters set-valued vector optimization problems is obtained.The sixth chapter summarizes the research results of the whole paper,and puts forward some unresolved problems to be further studied in the future.