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Sensitivity Analysis of Two Classes of Perturbation Maps

Author: LiaoChunMei
Tutor: LiShengJie
School: Chongqing University
Course: Computational Mathematics
Keywords: Generalized perturbation maps parametric set-valued optimization problems sensitivity properties second-order differentiability order semicontinuity
CLC: O174
Type: Master's thesis
Year: 2011
Downloads: 12
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Abstract


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.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Theory of functions
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