This new edition covers the central concepts of practical optimization
techniques, with an emphasis on methods that are both state-of-the-art
and popular. One major insight is the connection between the purely
analytical character of an optimization problem and the behavior of
algorithms used to solve a problem. This was a major theme of the first
edition of this book and the fourth edition expands and further
illustrates this relationship. As in the earlier editions, the material
in this fourth edition is organized into three separate parts. Part I is
a self-contained introduction to linear programming. The presentation in
this part is fairly conventional, covering the main elements of the
underlying theory of linear programming, many of the most effective
numerical algorithms, and many of its important special applications.
Part II, which is independent of Part I, covers the theory of
unconstrained optimization, including both derivations of the
appropriate optimality conditions and an introduction to basic
algorithms. This part of the book explores the general properties of
algorithms and defines various notions of convergence. Part III extends
the concepts developed in the second part to constrained optimization
problems. Except for a few isolated sections, this part is also
independent of Part I. It is possible to go directly into Parts II and
III omitting Part I, and, in fact, the book has been used in this way in
many universities.
New to this edition is a chapter devoted to Conic Linear Programming, a
powerful generalization of Linear Programming. Indeed, many conic
structures are possible and useful in a variety of applications. It must
be recognized, however, that conic linear programming is an advanced
topic, requiring special study. Another important topic is an
accelerated steepest descent method that exhibits superior convergence
properties, and for this reason, has become quite popular. The proof of
the convergence property for both standard and accelerated steepest
descent methods are presented in Chapter 8. As in previous editions,
end-of-chapter exercises appear for all chapters.
From the reviews of the Third Edition:
"... this very well-written book is a classic textbook in Optimization.
It should be present in the bookcase of each student, researcher, and
specialist from the host of disciplines from which practical
optimization applications are drawn." (Jean-Jacques Strodiot,
Zentralblatt MATH, Vol. 1207, 2011)
