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, this 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 simple, intuitive interpretations on complex, infinite–dimensional problems. The 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
∗ Local 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.
Linear Operators and Adjoints.
Optimization of Functionals.
Global Theory of Constrained Optimization.
Local Theory of Constrained Optimization.
Iterative Methods of Optimization.