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Titlebook: Abstract Convexity and Global Optimization; Alexander Rubinov Book 2000 Springer Science+Business Media Dordrecht 2000 Approximation.Conve

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發(fā)表于 2025-3-21 16:57:16 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
期刊全稱Abstract Convexity and Global Optimization
影響因子2023Alexander Rubinov
視頻videohttp://file.papertrans.cn/144/143447/143447.mp4
學(xué)科分類Nonconvex Optimization and Its Applications
圖書封面Titlebook: Abstract Convexity and Global Optimization;  Alexander Rubinov Book 2000 Springer Science+Business Media Dordrecht 2000 Approximation.Conve
影響因子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
Pindex Book 2000
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發(fā)表于 2025-3-21 22:00:31 | 只看該作者
Masego Katisi,Philip Jefferies,Mpho Sebakof this function is a closed normal subset of the cone ?., hence there exists an IPH function . defined on ?. such that hyp .. is the support set of . with respect to the set . of all min-type functions. This observation allows us to examine decreasing functions with the help of IPH functions (See Section 3.4).
板凳
發(fā)表于 2025-3-22 02:54:22 | 只看該作者
Book 2000nd 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. Howeve
地板
發(fā)表于 2025-3-22 07:51:14 | 只看該作者
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978-1-4419-4831-1Springer Science+Business Media Dordrecht 2000
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發(fā)表于 2025-3-23 02:46:32 | 只看該作者
https://doi.org/10.1007/978-3-319-72899-5One of the main results of convex analysis states that an arbitrary lower semicontinuous convex function . (perhaps admitting the value +∞) is the . of the set of all its affine minorants: ..
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發(fā)表于 2025-3-23 05:59:30 | 只看該作者
Ozge Karadag Caman MD, MSPH, PhDAbstract convexity based on the set of linear functions defined on ?. (as the set of elementary functions) leads to the classical convex analysis.
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