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/homepage/sac/cam/na2000/index.html7-Volume Set now available at
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In one of the papers in this collection, the remark that "nothing
at all takes place in the universe in which some rule of maximum of
minimum does not appear" is attributed to no less an authority than
Euler. Simplifying the syntax a little, we might paraphrase this as
"Everything is an optimization problem." While this might be
something of an overstatement, the element of exaggeration is
certainly reduced if we consider the extended form: "Everything is
an optimization problem or a system of equations." This
observation, even if only partly true, stands as a fitting
testimonial to the importance of the work covered by this
volume.
Since the 1960s, much effort has gone into the development and
application of numerical algorithms for solving problems in the two
areas of optimization and systems of equations. As a result, many
different ideas have been proposed for dealing efficiently with
(for example) severe nonlinearities and/or very large numbers of
variables. Libraries of powerful software now embody the most
successful of these ideas, and one objective of this volume is to
assist potential users in choosing appropriate software for the
problems they need to solve. More generally, however, these
collected review articles are intended to provide both researchers
and practitioners with snapshots of the 'state-of-the-art' with
regard to algorithms for particular classes of problem. These
snapshots are meant to have the virtues of immediacy through the
inclusion of very recent ideas, but they also have sufficient depth
of field to show how ideas have developed and how today's research
questions have grown out of previous solution attempts.
The most efficient methods for "local optimization, " both
unconstrained and constrained, are still derived from the classical
Newton approach.
As well as dealing in depth with the various classical, or
neo-classical, approaches, the selection of papers on optimization
in this volume ensures that newer ideas are also well
represented.
Solving nonlinear algebraic systems of equations is closely related
to optimization. The two are not completely equivalent, however,
and usually something is lost in the translation.
Algorithms for nonlinear equations can be roughly classified as
"locally convergent" or "globally convergent." The characterization
is not perfect.
Locally convergent algorithms include Newton's method, modern
quasi-Newton variants of Newton's method, and trust region methods.
All of these approaches are well represented in this volume.
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