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 = "75129",
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
derivativesgradients, Jacobians, Hessians, and so forthencountered 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
timedependent and steadystate partial differential equations. Alternatives to the handcoding of
derivatives are finite differences and automatic differentiation, both of which save programming
time at the possible cost of runtime efficiency.",
ad_tools = "TAMC"
}
