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Primal-Dual Interior-Point Methods

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by Stephen J. Wright


1997 / xx + 289 pages / Softcover / ISBN: 978-0-898713-82-4 / List Price $76.00 / SIAM Member Price $53.20 / Order Code OT54

"The current hottest topic in optimization is interior-point methods. Steve Wright, a renowned expert in optimization, has written a truly excellent introduction to this topic. We have used this book in a term-long seminar. It was immediately obvious that this book is both comprehensive and "very readable" to both experts and students new to this area. The book is not just a theoretical text but contains algorithms in enough detail to allow students to write efficient code. Even though the area of interior-points is still under development, this book promises to be an important reference for many years to come." -Professor Henry Wolkowicz, University of Waterloo

"This is a beautifully crafted book on a specialized but very important topic. Primal-dual methods are now recognized by both theoreticians and practitioners as the best available interior-point methods for linear programming. Steve Wright's book is remarkable because it demystifies a very active current research area, synthesizing the important contributions and making the many clever ideas underlying the subject accessible to graduate (or even good undergraduate) students.The book is comprehensive and beautifully written. I could not find a single poorly written sentence or confusing equation. I strongly recommend it to anyone interested in linear programming." -Michael Overton, New York University

"Stephen J. Wright has written an excellent book about primal-dual interior-point methods. The book covers major theoretical developments of the the last ten years as well as practical issues related to implementation of the methods. The subject is presented thoroughly, and valuable insight and motivation are also provided. The book can be used as an introduction to interior-point methods for advanced students and is a useful reference book for researchers. I am sure I am going to use the book a lot and cite it often." -Erling D. Andersen, Department of Management, Odense University, Denmark.

In the past decade, primal-dual algorithms have emerged as the most important and useful algorithms from the interior-point class. This book presents the major primal-dual algorithms for linear programming in straightforward terms. A thorough description of the theoretical properties of these methods is given, as are a discussion of practical and computational aspects and a summary of current software. This is an excellent, timely, and well-written work.

The major primal-dual algorithms covered in this book are path-following algorithms (short- and long-step, predictor-corrector), potential-reduction algorithms, and infeasible-interior-point algorithms. A unified treatment of superlinear convergence, finite termination, and detection of infeasible problems is presented. Issues relevant to practical implementation are also discussed, including sparse linear algebra and a complete specification of Mehrotra's predictor-corrector algorithm. Also treated are extensions of primal-dual algorithms to more general problems such as monotone complementarity, semidefinite programming, and general convex programming problems.

Some background in linear programming and its associated duality theory, linear algebra, and numerical analysis is helpful, although an extensive appendix ensures that the book is largely self-contained. The book will be useful for graduate students and researchers in the sciences and engineering who are interested in using large-scale optimization techniques in their research, including those interested in pursuing original research in interior point methods. Engineers may also find applications to problems of process control, predictive control, or design optimization. The book may also be used as a text for a special topics course in optimization or a unit of a general course in optimization or linear programming. Researchers and students in the field of interior-point methods will find the book invaluable as a reference to the key results, the basic techniques of analysis in the area, and the current state of the art.

Preface; Notation; Chapter 1: Introduction. Linear Programming; Chapter 2: Background: Linear Programming and Interior-Point Methods; Chapter 3: Complexity Theory; Chapter 4: Potential-Reduction Methods; Chapter 5: Path-Following Algorithms; Chapter 6: Infeasible-Interior-Point Algorithms; Chapter 7: Superlinear Convergence and Finite Termination; Chapter 8: Extensions; Chapter 9: Detecting Infeasibility; Chapter 10: Practical Aspects of Primal-Dual Algorithms; Chapter 11: Implementations; Notes and References; Appendix A: Basic Concepts and Results; Appendix B: Software Packages; Bibliography; Index.

ISBN: 9780898713824

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