Optimization by Vector Space Methods

Series in Decision and Control

by David G. Luenberger

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.

Genres: Mathematics, Textbooks, Computer Science

352 pages, Paperback

First published January 1, 1969

Reviews

[5dd]

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.

[Taylor Shiroff]

unironically one of the best things I’ve read (admittedly not in its entirety) in a while. not sure if that says more about me or the book tho

[Carol M.]

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.