ON AUTOMATIC DIFFERENTIATION AND ALGORITHMIC LINEARIZATION

Pesquisa Operacional

Andreas Griewank¹ 

关键词: Jacobians;    Taylor expansions;    piecewise linearization;   

DOI  :  10.1590/0101-7438.2014.034.03.0621

来源: SciELO

【 摘 要 】

We review the methods and applications of automatic differentiation, a research and development activity, which has evolved in various computational fields since the mid 1950's. Starting from very simple basic principles that are familiar from school, one arrives at various theoretical and practical challenges. The resulting activity encompasses mathematical research and software development; it is now oftenreferredtoas algorithmic differentiation. From a geometrical and algebraic point of view, differentiation amounts to linearization, a concept that naturally extends to infinite dimensional spaces. In contract to other surveys, we will emphasize this interpretation as it has become more important recently and also facilitates the treatment of nonsmooth problems by piecewise linearization.

【 授权许可】

CC BY   
 All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License