During the last decade the techniques of non-linear optim- ization have
emerged as an important subject for study and research. The increasingly
widespread application of optim- ization has been stimulated by the
availability of digital computers, and the necessity of using them in
the investigation of large systems. This book is an introduction to
non-linear methods of optimization and is suitable for undergraduate and
post- graduate courses in mathematics, the physical and social sciences,
and engineering. The first half of the book covers the basic
optimization techniques including linear search methods, steepest
descent, least squares, and the Newton-Raphson method. These are
described in detail, with worked numerical examples, since they form the
basis from which advanced methods are derived. Since 1965 advanced
methods of unconstrained and constrained optimization have been
developed to utilise the computational power of the digital computer.
The second half of the book describes fully important algorithms in
current use such as variable metric methods for unconstrained problems
and penalty function methods for constrained problems. Recent work, much
of which has not yet been widely applied, is reviewed and compared with
currently popular techniques under a few generic main headings. vi
PREFACE Chapter I describes the optimization problem in mathemat- ical
form and defines the terminology used in the remainder of the book.
Chapter 2 is concerned with single variable optimization. The main
algorithms of both search and approximation methods are developed in
detail since they are an essential part of many multi-variable methods.
