| Sensitivity analysis of set-valued equilibrium problems is an important part of set-valued optimization theory researching.In this thesis,we study the variational sets of perturbation maps and applications to sensitivity analysis,the sensitivity of the set-valued equilibrium problems and the higher-order sensitivity for the setvalued vector optimization problems.And the main contents are as follows:1.Firstly,we introduce the higher-order variational compact and higher-order quasi variational compact of type 2,and we establish a few relations between variational sets of a set-valued map and those of its profile map,including relations between proper minima of these variational sets.Then,we give an objective map and establish the relations between the variational sets/quasi variational sets of this objective map and that of the proper perturbation map.Meanwhile,we also establish the relations between the variational sets of this objective map and that of the weak perturbation map.2.We study the sensitivity of the parametric set-valued equilibrium problems.Firstly,we introduce the chain and sum rules of the first-order variational sets of type2,and some of the obtained results improve or generalize the corresponding ones in some literatures.Then,by virtue of the variational sets of type 2,we establish the first-order sensitivity results of variational inequalities.Finally,in terms of these sets,we establish the first-order sensitivity results for parametric set-valued equilibrium problems under the weak e ciency.3.Since the set-valued vector optimization problem is a special case of set-valued equilibrium problem,we further study the higher-order sensitivity in set-valued vector optimization problems.Firstly,we introduce the higher-order weak lower inner Studniarski epiderivatives of set-valued maps,and discuss some basic properties of the epiderivatives.Secondly,we discuss relationships between higher-order weak lower inner Studniarski epiderivatives of set-valued maps and their epigraphic maps.Then,given a family of parametrized vector optimization problems,we define a perturbation map and a weak perturbation map for the problems,respectively.Finally,we investigate the relationship between higher-order weak lower Studniarski epiderivatives for the weak perturbation maps and weakly minimal point sets for higher-order weak lower Studniarski epiderivatives of feasible set maps in the objective space.Meanwhile,we also investigate the relationships between higher-order weak lower Studniarski epiderivatives for the perturbation maps and two types of minimal point sets(i.e.minimal point sets and weakly minimal point sets)for higher-order weak lower Studniarski epiderivatives of feasible set maps in the objective space. |
