The Coderivatives Of A Piecewise Linear Function

Considering the extreme importance of subdifferential and coderivatives in variational analysis and the extreme difficulty and complexity of estimating subdifferentiatial and coderivatives of general nonsmooth mappings,this thesis considers the estimation and calculation of coderivatives and subdifferential of piecewise linear function class with good properties and wide representation.Based on the classification and representation of piecewise linear mappings recently established by Zheng and Yang,this thesis gives formulation of the Fréchet coderivatives of piecewise linear mappings.In addition,using the methods and techniques of variational analysis,we also give the quantitative estimation of Mordukhovich subdifferential of piecewise linear function.