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Numerical Analysis 2000 : Volume 4 - Watson

Numerical Analysis 2000

Volume 4

Paperback Published: 28th March 2001
ISBN: 9780444505996
Number Of Pages: 384

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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.

Preface: Numerical Analysis 2000. Vol. IV: Optimization and Nonlinear Equationsp. ix
Historical developments in convergence analysis for Newton's and Newton-like methodsp. 1
The theory of Newton's methodp. 25
A survey of truncated-Newton methodsp. 45
Variable metric methods for unconstrained optimization and nonlinear least squaresp. 61
Practical quasi-Newton methods for solving nonlinear systemsp. 97
Sequential quadratic programming for large-scale nonlinear optimizationp. 123
Trust region model management in multidisciplinary design optimizationp. 139
ABS algorithms for linear equations and optimizationp. 155
Automatic differentiation of algorithmsp. 171
Direct search methods: then and nowp. 191
Recent developments and trends in global optimizationp. 209
Numerical continuation methods: a perspectivep. 229
Piecewise linear methods for nonlinear equations and optimizationp. 245
Interval mathematics, algebraic equations and optimizationp. 263
Interior-point methodsp. 281
Complementarity problemsp. 303
Evolution and state-of-the-art in integer programmingp. 319
Combinatorial optimization: Current successes and directions for the futurep. 341
Optimal controlp. 361
Author Indexp. 373
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780444505996
ISBN-10: 0444505997
Series: Numerical Analysis 2000 : Book 4
Audience: General
Format: Paperback
Language: English
Number Of Pages: 384
Published: 28th March 2001
Country of Publication: NL
Dimensions (cm): 27.94 x 20.96  x 2.01
Weight (kg): 0.86

Earn 412 Qantas Points
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