TY - JOUR
A1 - Griewank, Andreas
A1 - Streubel, Tom
A1 - Lehmann, Lutz
A1 - Radons, Manuel
A1 - Hasenfelder, Richard
T1 - Piecewise linear secant approximation via algorithmic piecewise differentiation
T2 - Optimization Methods and Software
N2 - It is shown how piecewise differentiable functions F : IR^n -> IR^m that are defined by evaluation programmes can be approximated locally by a piecewise linear model based on a pair of sample points \check x and \hat x. We show that the discrepancy between function and model at any point x is of the bilinear order O(||x - \check x||*||x - \hat x||). As an application of the piecewise linearization procedure we devise a generalized Newton's method based on successive piecewise linearization and prove for it sufficient conditions for convergence and convergence rates equalling those of semismooth Newton. We conclude with the derivation of formulas for the numerically stable implementation of the aforedeveloped piecewise linearization methods.
Y1 - 2017
UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/6630
VL - 33
IS - 4-6
SP - 1108
EP - 1126
PB - Taylor & Francis
ER -