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＜電子ブック＞
Abstract Convexity and Global Optimization / by Alexander M. Rubinov
(Nonconvex Optimization and Its Applications ; 44)

版	1st ed. 2000.
出版者	(New York, NY : Springer US : Imprint: Springer)
出版年	2000
本文言語	英語
大きさ	XVIII, 493 p : online resource
著者標目	*Rubinov, Alexander M author SpringerLink (Online service)
件　名	LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:Mathematical models LCSH:Electrical engineering FREE:Calculus of Variations and Optimization FREE:Optimization FREE:Mathematical Modeling and Industrial Mathematics FREE:Electrical and Electronic Engineering
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-1-4757-3200-9

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