Automatic Differentiation of Algorithms: From Simulation to by Wolfram Klein, Andreas Griewank, Andrea Walther (auth.),

By Wolfram Klein, Andreas Griewank, Andrea Walther (auth.), George Corliss, Christèle Faure, Andreas Griewank, Laurent Hascoët, Uwe Naumann (eds.)

Automatic Differentiation (AD) is a maturing computational expertise and has turn into a mainstream instrument utilized by working towards scientists and desktop engineers. The swift boost of computing energy and advert instruments has enabled practitioners to quick generate derivative-enhanced models in their code for a huge variety of purposes in utilized learn and development.
Automatic Differentiation of Algorithms offers a accomplished and authoritative survey of all fresh advancements, new ideas, and instruments for advert use. The publication covers all points of the topic: arithmetic, medical programming (i.e., use of adjoints in optimization) and implementation (i.e., reminiscence administration problems). a powerful subject matter of the booklet is the relationships among advert instruments and different software program instruments, equivalent to compilers and parallelizers. A wealthy number of major functions are provided in addition, together with optimum-shape layout difficulties, for which advert deals extra effective instruments and techniques.

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Automatic Differentiation of Algorithms: From Simulation to Optimization

Computerized Differentiation (AD) is a maturing computational expertise and has turn into a mainstream device utilized by practising scientists and desktop engineers. The fast strengthen of computing strength and advert instruments has enabled practitioners to fast generate derivative-enhanced types in their code for a wide diversity of functions in utilized learn and improvement.

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2) fk(X), k=l where the component functions fk : lRn r--+ lR are such that the extended function has a sparse Jacobian matrix. Our techniques are geared to the solution of large-scale optimization problems. For an extensive treatment of techniques for computing derivatives of general and partially separable functions with automatic differentiation tools, we recommend the recent book by Griewank [238]. Griewank and Toint [248] introduced partially separable functions, showing that if the Hessian matrix \7 2 f (x) is sparse, then f : lRn r--+ lR is partially separable.

Lobel and R. Altpeter, Siemens KWU. 2 Automatic Differentiation Tools in Optimization Software Jorge J. More ABSTRACT We discuss the role of automatic differentiation tools in optimization software. We emphasize issues that are important to large-scale optimization and that have proved useful in the installation of nonlinear solvers in the NEOS Server. Our discussion centers on the computation of the gradient and Hessian matrix for partially separable functions and shows that the gradient and Hessian matrix can be computed with guaranteed bounds in time and memory requirements.

The detection of common subexpressions within different functions and/or derivatives is very hard to do automatically. It might be achieved through peep hole optimization of the compiler on the original code but may fail on the enhanced code, where the original statements are spread further apart. An additional optimization of the functional description of the current and charge functions of the transistor models with respect to the understanding of the results of the previous attempt was done in a further step.

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