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Series in Decision and Control
Optimization by Vector Space Methods
ACE ISBN 047118117X (ISBN13: 9780471181170)
Unifies the field of optimization with a few geometric principles
The number of books that can legitimately be called classics in their fields is small indeed, but David Luenberger's OPtimization by Vector Space Methods certainly qualifies. Not only does Luenberger clearly demonstrate that a large segment of the field of optimization can be effectively unified by a few geometric principles of linear vector space theory, but his methods have found applications quite removed from the engineering problems to which they were first applied. Nearly 30 years after its initial publication, athis book is still among the most frequently cited sources in books and articles on financial optimization.
the book uses functional analysis--the study of linear vector spaces--to impose problems. Thea early chapters offer an introduction to functional analysis, with applications to optimization. Topics addressed include linear space, Hilbert space, least-squares estimation, dual spaces, and linear operators and adjoints. Later chapters deal explicitly with optimization theory, discussing:
Optimization of functionals
Global theory of constrained optimization
Iterative methods of optimization
End-of-chapter problems constitute a major component of this book and come in two basic varieties. The first consists of miscellaneous mathematical problems and proofs that extend and supplement the theoretical material in the text; the second, optimization problems, illustrates further areas of application and helps the reader formulate and solve practical problems.
For professionals and graduate students in engineering, mathematics, operations research, economics, and business and finance, Optimization by Vector Space Methods is an indispensable source of problem-solving tools
--back cover
Unifies the field of optimization with a few geometric principles
The number of books that can legitimately be called classics in their fields is small indeed, but David Luenberger's OPtimization by Vector Space Methods certainly qualifies. Not only does Luenberger clearly demonstrate that a large segment of the field of optimization can be effectively unified by a few geometric principles of linear vector space theory, but his methods have found applications quite removed from the engineering problems to which they were first applied. Nearly 30 years after its initial publication, athis book is still among the most frequently cited sources in books and articles on financial optimization.
the book uses functional analysis--the study of linear vector spaces--to impose problems. Thea early chapters offer an introduction to functional analysis, with applications to optimization. Topics addressed include linear space, Hilbert space, least-squares estimation, dual spaces, and linear operators and adjoints. Later chapters deal explicitly with optimization theory, discussing:
Optimization of functionals
Global theory of constrained optimization
Iterative methods of optimization
End-of-chapter problems constitute a major component of this book and come in two basic varieties. The first consists of miscellaneous mathematical problems and proofs that extend and supplement the theoretical material in the text; the second, optimization problems, illustrates further areas of application and helps the reader formulate and solve practical problems.
For professionals and graduate students in engineering, mathematics, operations research, economics, and business and finance, Optimization by Vector Space Methods is an indispensable source of problem-solving tools
--back cover
326 pages, Paperback
First published January 1, 1969
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Displaying 1 - 2 of 2 reviews
December 19, 2012
Luenberger's talent for balancing mathematical rigor with clear and intuitive descriptions is truly amazing. Not only is this book a masterful treatment of optimization, but it is also the best introduction to functional analysis I've ever seen.
I can describe the book as "clear and concise," but that doesn't begin to do it justice. This book has everything it needs and absolutely nothing that it doesn't, yet Luenberger somehow achieves this without falling prey to the dry and lifeless format of theory-proof, theory-proof that is common to most advanced math books. This is one of the very few math books I've ever read that is actually engaging. It reads like a carefully constructed and mathematically elegant "story". One in which, when you reach the end, you look back with surprise at the enormous amount of useful information you've absorbed.
It is quite simply the best math book I have ever read.
I can describe the book as "clear and concise," but that doesn't begin to do it justice. This book has everything it needs and absolutely nothing that it doesn't, yet Luenberger somehow achieves this without falling prey to the dry and lifeless format of theory-proof, theory-proof that is common to most advanced math books. This is one of the very few math books I've ever read that is actually engaging. It reads like a carefully constructed and mathematically elegant "story". One in which, when you reach the end, you look back with surprise at the enormous amount of useful information you've absorbed.
It is quite simply the best math book I have ever read.
June 15, 2014
A gem of a book! Could have been named "Optimization in Finite and Infinite Dimensions, with Introduction to Functional Analysis." Even if you're not in Operations Research or controls, get this book if you'd like to see a different "take" on Hilbert Space etc. than what you've seen in physics (or wherever...).
In fact, you can use this book as your very first intro to Functional Analysis if you've not had a course in that subject. It's friendly and very well structured and easy to use on one's own.
In fact, you can use this book as your very first intro to Functional Analysis if you've not had a course in that subject. It's friendly and very well structured and easy to use on one's own.
Displaying 1 - 2 of 2 reviews