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Titlebook: Conjugate Gradient Algorithms in Nonconvex Optimization; Radosław Pytlak Book 2009 Springer-Verlag Berlin Heidelberg 2009 Algebra.Bound Co

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发表于 2025-3-21 18:27:50 | 显示全部楼层 |阅读模式
书目名称Conjugate Gradient Algorithms in Nonconvex Optimization
编辑Radosław Pytlak
视频video
概述Includes supplementary material:
丛书名称Nonconvex Optimization and Its Applications
图书封面Titlebook: Conjugate Gradient Algorithms in Nonconvex Optimization;  Radosław Pytlak Book 2009 Springer-Verlag Berlin Heidelberg 2009 Algebra.Bound Co
描述.This up-to-date book is on algorithms for large-scale unconstrained and bound constrained optimization. Optimization techniques are shown from a conjugate gradient algorithm perspective. ..Large part of the book is devoted to preconditioned conjugate gradient algorithms. In particular memoryless and limited memory quasi-Newton algorithms are presented and numerically compared to standard conjugate gradient algorithms. ..The special attention is paid to the methods of shortest residuals developed by the author. Several effective optimization techniques based on these methods are presented. ..Because of the emphasis on practical methods, as well as rigorous mathematical treatment of their convergence analysis, the book is aimed at a wide audience. It can be used by researches in optimization, graduate students in operations research, engineering, mathematics and computer science. Practitioners can benefit from numerous numerical comparisons of professional optimization codes discussed in the book. .
出版日期Book 2009
关键词Algebra; Bound Constrained Optimization; Conjugate Gradient Algorithms; Continuous Optimization; Large
版次1
doihttps://doi.org/10.1007/978-3-540-85634-4
isbn_softcover978-3-642-09925-0
isbn_ebook978-3-540-85634-4Series ISSN 1571-568X
issn_series 1571-568X
copyrightSpringer-Verlag Berlin Heidelberg 2009
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发表于 2025-3-21 23:39:13 | 显示全部楼层
1571-568X mathematics and computer science. Practitioners can benefit from numerous numerical comparisons of professional optimization codes discussed in the book. .978-3-642-09925-0978-3-540-85634-4Series ISSN 1571-568X
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Phase Domains and Phase Solitons,iable problems were proposed. These propositions relied on the simplicity of their counterparts for quadratic problems. As we have shown in the previous chapter a conjugate gradient algorithm is an iterative process which requires at each iteration the current gradient and the previous direction. Th
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Subcritical Solitons I: Saturable Absorber, preconditioned conjugate gradient algorithms by others. The purpose of scaling in methods applied to quadratics is to transform eigenvalues of the Hessian matrix. Theorem 1.11 suggests that if eigenvalues are clustered then a conjugate gradient algorithm minimizes the quadratic in the number of ite
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Todd Shelly,Nancy Epsky,Roger Vargason. The idea behind preconditioned conjugate gradient algorithm is to transform the decision vector by linear transformation . such that after the transformation the nonlinear problem is . to solve — eigenvalues of Hessian matrices of the objective function of the new optimization problem are more c
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https://doi.org/10.1007/978-3-540-36308-8duals which uses the projection operator to cope with box constraints is competitive to the benchmark code L-BFGS-B in terms of CPU time (cf. Figs. 10.1, 10.2, 10.4, 10.6). For larger problems it is almost as efficient as L-BFGS-B program also in terms of the number of function evaluations (cf. Fig.
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Fundamental tests with trapped antiprotons,The method of shortest residuals is briefly discussed in Chap. 1. We show there that the method differs from a standard conjugate gradient algorithm only by scaling factors applied to conjugate directions. This is true when problems with quadratics are considered. However, these methods are quite different if applied to nonconvex functions.
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