Abstract Convexity and Global Optimization by Alexander M Rubinov

Abstract Convexity and Global Optimization by Alexander M Rubinov

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.

'This book, written by one of the leading contributors in the field, is an up-to-date and very valuable referenceIt will be precious to any researcher working in the field on theoretical aspects and applications as well. It opens new ways in global optimization.'
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)

SKU	Unavailable
ISBN 13	9781441948311
ISBN 10	1441948317
Title	Abstract Convexity and Global Optimization
Author	Alexander M Rubinov
Series	Nonconvex Optimization And Its Applications
Condition	Unavailable
Binding Type	Paperback
Publisher	Springer-Verlag New York Inc.
Year published	2010-12-01
Number of pages	493
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.