by Dimitri P. Bertsekas
Publication: 1999, 794 pages, hardcover
Contents, Preface, Ordering, Home
This is a substantially expanded (by 130 pages) and improved edition of our best-selling nonlinear programming book. The treatment focuses on iterative algorithms for constrained and unconstrained optimization, Lagrange multipliers and duality, large scale problems, and on the interface between continuous and discrete optimization.
Nearly 40% of the new material represents miscellaneous additions scattered throughout the text. The remainder deals with three new topics. These are:
A new section in Chapter 3 that focuses on a simple but far-reaching treatment of Fritz John necessary conditions and constraint qualifications, and also includes semi-infinite programming.
A new section in Chapter 5 on the use of duality and Lagrangian relaxation for solving discrete optimization problems. This section describes several motivating applications, and provides a connecting link between continuous and discrete optimization.
A new section in Chapter 6 on approximate and incremental subgradient methods. This material is the subject of ongoing research, but it was thought sufficiently significant to be included in summary here.
A new internet-based feature was added to the book, which significantly extends its scope and coverage. Many of the theoretical exercises, quite a few of them new, have been solved in detail and their solutions have been posted on the internet (see below).
The latest (April 2004) printing of the second edition (the only one being sold) corrects typos, includes a few more exercises, and brings the book in closer harmony with the companion work Convex Analysis and Optimization book (Athena Scientific, 2003). Quite a few sections were modified and even substantially rewritten. Significant changes in content are the following:
The addition of new research material on existence of optimal solutions in Section 2.1.
The introduction of the notion of pseudonormality in Section 3.3.5.
A discussion of the EM algorithm in Section 5.4.6.
A more detailed presentation of convex analysis in Appendix B.
From the review by Olvi Mangasarian (Optima, March 1997):
"This is a beautifully written book by a prolific author ... who has taken
painstaking care in making the presentation extremely lucid ... The style is
unhurried and intuitive yet mathematically rigorous."
"The numerous figures in the book are extremely well thought out and are
used in a very effective way to elucidate the text. The detailed and
self-explanatory long captions accompanying each figure are extremely
"The 80 pages constituting the four appendixes serve as a masterfully
written introduction to the field of nonlinear programming that can be used
as a self-contained monograph. Teachers using this book could easily assign
these appendixes as introductory or remedial material."
"This book contains a wealth of material... Throughout this book, well-prepared graphics illustrate ideas and results.
The text contains many examples and each section is followed by a set of nice exercises."
provides extensive coverage of iterative optimization methods within a unifying framework
provides a detailed treatment of interior point methods for linear programming
covers in depth duality theory from both a variational and a geometrical/convex analysis point of view
includes much new material on a number of topics, such as neural network training, discrete-time optimal control, and large-scale optimization
includes a large number of examples and exercises detailed solutions of many of which are posted on the internet (see below)
developed through extensive classroom use in first-year graduate courses
The author is McAfee Professor of Engineering at the Massachusetts Institute of Technology and a member of the prestigious US National Academy of Engineering. He is the recipient of the 2001 A. R. Raggazini ACC education award and the 2009 INFORMS expository writing award. He has been teaching the material included in this book in introductory graduate courses for over thirty years.
The material listed below can be freely downloaded, reproduced, and distributed .