Sensitivity Analysis Of Two Classes Of Perturbation Maps

In this thesis, second-order sensitivity properties of generalized perturbation maps and sensitivity properties of parametric set-valued optimization problems in Banach spaces are discussed.At first, the concepts of second-order proto-differentiability, second-order semidifferentiability and second-order lower semidifferentiability for set-valued maps are introduced. Then, by using them, second-order differential properties of a class of set-valued maps are investigated and an explicit expression of the second-order derivatives is obtained. Moreover, second-order sensitivity properties are discussed for generalized perturbation maps.At the same time, by virtue of order semicontinuity and local order semicontinuity for set-valued maps, an explicit expression of the coderivatives for the addition of a set-valued map and a cone is obtained. Then, combining the obtained results, sensitivity properties of parametric set-valued optimization problems in Banach spaces are discussed.