Abstract Convexity and Global Optimization
Language: English
Published by Springer US, 2000
- Hardcover
- New
Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH
AbeBooks seller since August 14, 2006
Condition: New
£ 157.39
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Add to basketItem description from seller
Druck auf Anfrage Neuware - Printed after ordering - Special tools are required for examining and solving optimization problems. The main tools in the study of local optimization are classical calculus and its modern generalizions which form nonsmooth analysis. The gradient and various kinds of generalized derivatives allow us to ac complish a local approximation of a given function in a neighbourhood of a given point. This kind of approximation is very useful in the study of local extrema. However, local approximation alone cannot help to solve many problems of global optimization, so there is a clear need to develop special global tools for solving these problems. The simplest and most well-known area of global and simultaneously local optimization is convex programming. The fundamental tool in the study of convex optimization problems is the subgradient, which actu ally plays both a local and global role. First, a subgradient of a convex function f at a point x carries out a local approximation of f in a neigh bourhood of x. Second, the subgradient permits the construction of an affine function, which does not exceed f over the entire space and coincides with f at x. This affine function h is called a support func tion. Since f(y) ~ h(y) for ally, the second role is global. In contrast to a local approximation, the function h will be called a global affine support.…
Seller Inventory # 9780792363231
- Title
- Abstract Convexity and Global Optimization
- Author
- Alexander M. Rubinov
- Publisher
- Springer US
- Publication year
- 2000
- Condition
- Neu
- Binding
- Buch
- Language
- English
- ISBN 10
- 079236323X
- ISBN 13
- 9780792363231
- Item weight
- 882 grams
- Dimensions
- 241x160x33 mm
"Synopsis" may belong to another edition of this title.
Review
Mathematical Reviews (2002i)
'The book will be very useful for experts in optimisation and aspects of functional and numerical analysis and related topics. This is an excellent introduction to those who are interested in the study of abstract convexity and its applications and to very interesting and highly applicable generalisations on convexity.'
Australian Mathematical Society GAZETTE, August (2002)
"About the title" may belong to another edition of this title.
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