6630
2017
2018
eng
1108
1126
4-6
33
article
Taylor & Francis
0
2017-10-27
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Piecewise linear secant approximation via algorithmic piecewise differentiation
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.
Optimization Methods and Software
10.1080/10556788.2017.1387256
yes
urn:nbn:de:0297-zib-61642
Andreas Griewank
Tom Streubel
Tom Streubel
Lutz Lehmann
Manuel Radons
Richard Hasenfelder
Mathematical Optimization
MODAL-GasLab
Streubel, Tom
MODAL-Gesamt
Energy Network Optimization