Engineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems. Unifies the large field of optimization with a few geometric principles....
Engineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems. Unifies the large field of optimization with a few geometric principles. Covers functional analysis with a minimum of mathematics. Contains problems that relate to the applications in the book.
作者简介
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David G. Luenberger is a professor in the School of Engineering at Stanford University. He has published four textbooks and over 70 technical papers. Professor Luenberger is a Fellow of the Institute of Electrical and Electronics Engineers and recipient of the 1990 Bode Lecture Award. His current research is mainly in investment science, economics, and planning.
原文摘录
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Proposition 1. Let X be a Banach space, M a closed subspace of X, and X/M the quotient space with the quotient norm defined as above. Then X/M is also a Banach space. (查看原文)
Since the solution to the approximation problem is equivalent to solution to the normal equations, it is clear that the Gram-Schmidt procedure can be interpreted as a procedure for inverting the Gram matrix. Conversely, many effective algorithms for solving the normal equations have an interpretation in terms of the minimum norm problem in Hilbert space. (p. 63) (查看原文)
何进荣
6 有用 谁家的鸡 2020-02-25 20:22:51
这本书对duality的处理比任何一本我看过的其他书都更elegant。泛函分析观点下的optimization才是最自然的
5 有用 谜团 2014-01-20 18:23:06
泛函的框架下看优化，比较高的观点，由于成书较早，有些叙述有点过时。
3 有用 Eric Zhou 2018-04-20 21:42:31
基于泛函的优化理论，所有以前学过的优化方法都是这本书的特例...
2 有用 arcora 2024-01-14 10:50:11 北京
深刻，学扎实线性泛函和有研究经历之后才知道本书的价值
2 有用 Demon Hunter 2020-06-21 13:33:25
the more distinct are the things it connects