Publication: A Primer on Differentiation
Introduction
Applications
Tools
Research Groups
Workshops
Publications
   List Publications
   Advanced Search
   Info
   Add Publications
My Account
About

A Primer on Differentiation

- Article in a journal -
 

Author(s)
Mark S. Gockenbach

Published in
Optimization and Engineering

Year
2001

Abstract
The central idea of differential calculus is that the derivative of a function defines the best local linear approximation to the function near a given point. This basic idea, together with some representation theorems from linear algebra, unifies the various derivatives---gradients, Jacobians, Hessians, and so forth---encountered in engineering and optimization. The basic differentiation rules presented in calculus classes, notably the product and chain rules, allow the computation of the gradients and Hessians needed by optimization algorithms, even when the underlying operators are quite complex. Examples include the solution operators of time-dependent and steady-state partial differential equations. Alternatives to the hand-coding of derivatives are finite differences and automatic differentiation, both of which save programming time at the possible cost of run-time efficiency.

AD Tools
TAMC

AD Theory and Techniques
Introduction

BibTeX
@ARTICLE{
         Gockenbach2001APo,
       ad_theotech = "Introduction",
       author = "Mark S. Gockenbach",
       title = "A Primer on Differentiation",
       journal = "Optimization and Engineering",
       year = "2001",
       volume = "2",
       number = "1",
       pages = "75--129",
       abstract = "The central idea of differential calculus is that the derivative of a function
         defines the best local linear approximation to the function near a given point. This basic idea,
         together with some representation theorems from linear algebra, unifies the various
         derivatives---gradients, Jacobians, Hessians, and so forth---encountered in engineering and
         optimization. The basic differentiation rules presented in calculus classes, notably the product and
         chain rules, allow the computation of the gradients and Hessians needed by optimization algorithms,
         even when the underlying operators are quite complex. Examples include the solution operators of
         time-dependent and steady-state partial differential equations. Alternatives to the hand-coding of
         derivatives are finite differences and automatic differentiation, both of which save programming
         time at the possible cost of run-time efficiency.",
       ad_tools = "TAMC"
}


back
  

Contact:
autodiff.org
Username:
Password:
(lost password)