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 -