Set Order Relations And Scalarization In Set Optimization With Applications To Continuity And Robustness

The set-valued optimization problem refers to the extremum problem of set-value objective or constraint mappings,which is an important research model in vector optimization.Vector optimization criterion and set optimization criterion are two types of solution criteria for set-valued optimization,and the set-valued optimization problem based on set optimization criterion is called a set optimization problem.Abundant achievements have been made in the stability analysis of vector optimization problems,but the discussion about the semicontinuity of solution mappings for parametric set optimization problems that based on set order relations is limited and therefore has research significance.The robustness of uncertain multiobjective optimization problem is another important topic,which is closely related to set order relations and set optimization.The scalarization method is a powerful tool for vector and set-valued optimization.In this thesis,the solution continuity for parameter set optimization problems and the robust efficiency of uncertain multiobjective optimization under generalized set order relations are discussed respectively,by means of scalarization characterizations of generalized set order relations,and corresponding conclusions in the related literatures are extended.The main research contents are as follows:Firstly,for the generalized set order relations derived from ordering sets rather than ordering cones,with properties of recession cones,this thesis extends characterizations of generalized set order relations by the linear functional and the oriented distance function,by referring to the Gerstewitz function case.Based on the linear and nonlinear scalarization of generalized set order relations,new monotone-like concepts of the set-valued mapping are proposed,and semicontinuity results of solutions for parametric set optimization problems based on generalized set-orders are obtained.Secondly,with the help of the image space analysis method,the linear and nonlinear scalarization characterizations of generalized set order relations,and the idea of separation,the robust efficiency of uncertain multiobjective optimization problems which based on generalized set order relations is studied,and some equivalent characterizations of robust efficient solutions are obtained.