# Algorithmic Differentiation of Numerical Methods : Second-Order Tangent and Adjoint Solvers for Systems of Parametrized Nonlinear Equations

@inproceedings{Safiran2014AlgorithmicDO, title={Algorithmic Differentiation of Numerical Methods : Second-Order Tangent and Adjoint Solvers for Systems of Parametrized Nonlinear Equations}, author={Niloofar Safiran and Johannes Lotz and Uwe Naumann}, year={2014} }

Forward and reverse modes of algorithmic differentiation (AD) transform implementations of multivariate vector functions F : IR → IR as computer programs into tangent and adjoint code, respectively. The reapplication of the same ideas yields higher derivative code. In particular, second derivatives play an important role in nonlinear programming. Second-order methods based on Newton’s algorithm promise faster convergence in the neighbourhood of the minimum by taking into account second…

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