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Field name	Details
Dewey Class	515.64
Title	Abstract Convexity and Global Optimization ([EBook]) / by Alexander Rubinov.
Author	Rubinov, Aleksandr Moiseevič , 1940-
Other name(s)	SpringerLink (Online service)
Publication	Boston, MA : Springer US , 2000.
Physical Details	XVIII, 493 pages : online resource.
Series	Nonconvex Optimization and Its Applications 1571-568X ; ; 44
ISBN	9781475732009
Summary Note	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.:
Contents note	1. An Introduction to Abstract Convexity -- 3. Elements of Monotonic Analysis: Monotonic Functions -- 4. Application to Global Optimization: Lagrange and Penalty Functions -- 5. Elements of Star-Shaped Analysis -- 6. Supremal Generators and Their Applications -- 7. Further Abstract Convexity -- 8. Application to Global Optimization: Duality -- 9. Application to Global Optimization: Numerical Methods -- References.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4757-3200-9
Links to Related Works	Subject References: Calculus of variations . Calculus of variations and optimal control; optimization . Electrical engineering . Mathematical Modeling and Industrial Mathematics . Mathematical models . Mathematical optimization . Mathematics . Optimization . Authors: Rubinov, Aleksandr Moiseevič 1940- . Series: Nonconvex Optimization and Its Applications . Classification: 515.64 .

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Abstract Convexity and Global Optimization

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