Optimization by Vector Space Methods
Series: Wiley Professional Paperback Series; Series in Decision and Control
Publisher: John Wiley & Sons Inc
Published: 1969
Place of publication: New York, USA
Language: eng
Format: Paperback
Number of pages: 344
ISBN-13: 9780471181170
Copyright date: 1969
First sentence: The first few sections of this chapter introduce the concept of a vector space and explore the elementary properties resulting from the basic definition.
Description: 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
Table of contents: title: Linear Spaces.; title: Hilbert Space.; title: Least-Squares Estimation.; title: Dual Spaces.; title: Linear Operators and Adjoints.; title: Optimization of Functionals.; title: Global Theory of Constrained Optimization.; title: Local Theory of Constrained Optimization.; title: Iterative Methods of Optimization.; title: Indexes.