Piecewise linear secant approximation via algorithmic piecewise differentiation

@article{Griewank2018PiecewiseLS,
  title={Piecewise linear secant approximation via algorithmic piecewise differentiation},
  author={Andreas Griewank and Thomas Streubel and Lutz Lehmann and Manuel Radons and Richard Hasenfelder},
  journal={Optimization Methods and Software},
  year={2018},
  volume={33},
  pages={1108 - 1126}
}
It is shown how piecewise differentiable functions F:ℝn↦ℝm that are defined by evaluation programmes can be approximated locally by a piecewise linear model based on a pair of sample points . We show that the discrepancy between function and model at any point x is of the bilinear order . 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… 
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