Optimization by Vector Space Methods

David G. Luenberger
Pub: John Wiley and Sons, Inc. New York, 1969.

From the preface: The primary objective of this book is to demonstrate that a rather large segment of the field of optimization can be effectively unified by a few geometric principles of linear vector space theory. By the use of these principles, important and complex infinite-dimensional problems, such as those generated by consideration of time functions, are interpreted and solved by methods springing from our geometric insight. Concepts such as distance, orthogonality, and convexity play fundamental roles in this development. Viewed in these terms, seemingly diverse problems and techniques often are found to be intimately related.

CONTENTS

1. Introduction
2. Linear Spaces
3. Hilbert Space
4. Least-Squares Estimation
5. Dual Spaces
6. Linear Operators and Adjoints
7. Optimization of Functionals
8. Global Theory of Constrained Optimization
9. Local Theory of Constrained Optimization
10. Iterative Methods of Optimization