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Titlebook: Optimization; Kenneth Lange Textbook 20041st edition Springer-Verlag New York 2004 Analysis.Excel.Random variable.Statistical Methods.Stoc

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发表于 2025-3-21 20:07:04 | 显示全部楼层 |阅读模式
书目名称Optimization
编辑Kenneth Lange
视频video
概述The content of courses on optimization theory varies tremendously..This book views linear programming as a special case of nonlinear programming..The real bridge between linear and nonlinear programmi
丛书名称Springer Texts in Statistics
图书封面Titlebook: Optimization;  Kenneth Lange Textbook 20041st edition Springer-Verlag New York 2004 Analysis.Excel.Random variable.Statistical Methods.Stoc
描述.Finite-dimensional optimization problems occur throughout the mathematical sciences. The majority of these problems cannot be solved analytically. This introduction to optimization attempts to strike a balance between presentation of mathematical theory and development of numerical algorithms. Building on students’ skills in calculus and linear algebra, the text provides a rigorous exposition without undue abstraction. Its stress on convexity serves as bridge between linear and nonlinear programming and makes it possible to give a modern exposition of linear programming based on the interior point method rather than the simplex method....The emphasis on statistical applications will be especially appealing to graduate students of statistics and biostatistics. The intended audience also includes graduate students in applied mathematics, computational biology, computer science, economics, and physics as well as upper division undergraduate majors in mathematics who want to see rigorous mathematics combined with real applications....Chapter 1 reviews classical methods for the exact solution of optimization problems. Chapters 2 and 3 summarize relevant concepts from mathematical analy
出版日期Textbook 20041st edition
关键词Analysis; Excel; Random variable; Statistical Methods; Stochastic Processes; algorithms; expectation–maxim
版次1
doihttps://doi.org/10.1007/978-1-4757-4182-7
isbn_ebook978-1-4757-4182-7Series ISSN 1431-875X Series E-ISSN 2197-4136
issn_series 1431-875X
copyrightSpringer-Verlag New York 2004
The information of publication is updating

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The MM Algorithm,an optimization problem, (c) separating the variables of an optimization problem, (d) dealing with equality and inequality constraints gracefully, and (e) turning a nondifferentiable problem into a smooth problem. In simplifying the original problem, we must pay the price of iteration or iteration with a slower rate of convergence.
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Analysis of Convergence,icity. Scoring lies somewhere between Newton’s method and the MM algorithm. It tends to converge more quickly than the MM algorithm and to behave more stably than Newton’s method. Quasi-Newton methods also occupy this intermediate zone. Because the issues are complex, all of these algorithms survive and prosper in certain computational niches.
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Differentiation,tion of differentiability that avoids most of the pitfalls and makes differentiation of vectors and matrices relatively painless. In later chapters, this definition also improves the clarity of exposition.
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