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Series in Decision and Control
Optimization by Vector Space Methods
A classic in mathematical optimization, Optimization by Vector Space Methods presents a unified and rigorous approach to the theory of optimization through the language of vector spaces and functional analysis. Written by David G. Luenberger, a leading scholar in systems science and operations research, this foundational text bridges pure mathematics and applied optimization with clarity and depth.
The book introduces optimization problems in both finite- and infinite-dimensional spaces, emphasizing the geometric and algebraic structures that underlie modern methods. It develops the essential tools of vector space theory — including linear operators, duality, adjoint systems, and inner product spaces — and applies them to practical optimization models found in engineering, economics, and applied mathematics.
Balancing theory and intuition, Optimization by Vector Space Methods remains a cornerstone reference for graduate students, researchers, and professionals seeking a deep understanding of optimization in its most general form.
The book introduces optimization problems in both finite- and infinite-dimensional spaces, emphasizing the geometric and algebraic structures that underlie modern methods. It develops the essential tools of vector space theory — including linear operators, duality, adjoint systems, and inner product spaces — and applies them to practical optimization models found in engineering, economics, and applied mathematics.
Balancing theory and intuition, Optimization by Vector Space Methods remains a cornerstone reference for graduate students, researchers, and professionals seeking a deep understanding of optimization in its most general form.
Kindle Edition
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