Name: abstract convexity and global optimization (en Inglés)
Price: 140.43 USD
Availability: InStock
Author: Rubinov, Alexander M.
ISBN: 9781441948311

portada abstract convexity and global optimization (en Inglés)

abstract convexity and global optimization (en Inglés)

Formato

Libro Físico

Autor

Alexander M. Rubinov

Editorial

Springer

Año

2010

Idioma

Inglés

N° páginas

493

Encuadernación

Tapa Blanda

Dimensiones

23.9 x 16.5 x 3.3 cm

Peso

0.79 kg.

ISBN

1441948317

ISBN13

9781441948311

Categorías

Cálculo
Programación lineal
Matemáticas aplicadas

abstract convexity and global optimization (en Inglés)

Alexander M. Rubinov (Autor) · Springer · Tapa Blanda

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Reseña del libro "abstract convexity and global optimization (en Inglés)"

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.