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xviii P REFACE
designing a portfolio of investments to maximize expected return while maintaining
an acceptable level of risk;
controlling a chemical process or a mechanical device to optimize performance or
meet standards of robustness;
computing the optimal shape of an automobile or aircraft component.
Every year optimization algorithms are being called on to handle problems that
are much larger and complex than in the past. Accordingly, the book emphasizes large-
scale optimization techniques, such as interior-point methods, inexact Newton methods,
limited-memory methods, and the role of partially separable functions and automatic
differentiation. It treats important topics such as trust-region methods and sequential
quadratic programming more thoroughly than existing texts, and includes comprehensive
discussion of such “core curriculum” topics as constrained optimization theory, Newton
and quasi-Newton methods, nonlinear least squares and nonlinear equations, the simplex
method, and penalty and barrier methods for nonlinear programming.
The Audience
We intend that this book will be used in graduate-level courses in optimization, as of-
fered in engineering, operations research, computer science, and mathematics departments.
There is enough material here for a two-semester (or three-quarter) sequence of courses.
We hope, too, that this book will be used by practitioners in engineering, basic science, and
industry, and our presentation style is intended to facilitate self-study. Since the book treats
a number of new algorithms and ideas that have not been described in earlier textbooks, we
hope that this book will also be a useful reference for optimization researchers.
Prerequisites for this book include some knowledge of linear algebra (including nu-
merical linear algebra) and the standard sequence of calculus courses. To make the book as
self-contained as possible, we have summarized much of the relevant material from these ar-
eas in the Appendix. Our experience in teaching engineering students has shown us that the
material is best assimilated when combined with computer programming projects in which
the student gains a good feeling for the algorithms—their complexity, memory demands,
and elegance—and for the applications. In most chapters we provide simple computer
exercises that require only minimal programming proficiency.
Emphasis and Writing Style
We have used a conversational style to motivate the ideas and present the numerical
algorithms. Rather than being as concise as possible, our aim is to make the discussion flow
in a natural way. As a result, the book is comparatively long, but we believe that it can be
read relatively rapidly. The instructor can assign substantial reading assignments from the
text and focus in class only on the main ideas.
A typical chapter begins with a nonrigorous discussion of the topic at hand, including
figures and diagrams and excluding technical details as far as possible. In subsequent sections,