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Nonlinear Equations and Optimisation
Paperback
Series: Numerical Analysis 2000, Book 4
ISBN13: 9780444505996
Publisher: Elsevier
Published: Mar 14 2001
Pages: 384
Weight: 1.90
Height: 0.79 Width: 8.25 Depth: 11.00
Language: English
/homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price !
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.
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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