Linear & Nonlinear Programming

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)

David G. Luenberger received the B.S. degree from the California Institute of Technology and the M.S. and Ph.D. degrees from Stanford University, all in Electrical Engineering. Since 1963 he has been on the faculty of Stanford University. He helped found the Department of Engineering-Economic Systems, now merged to become the Department of Management Science and Engineering, where his is currently a professor.

He served as Technical Assistant to the President’s Science Advisor in 1971-72, was Guest Professor at the Technical University of Denmark (1986), Visiting Professor of the Massachusetts Institute of Technology (1976), and served as Department Chairman at Stanford (1980-1991).

His awards include: Member of the National Academy of Engineering (2008), the Bode Lecture Prize of the Control Systems Society (1990), the Oldenburger Medal of the American Society of Mechanical Engineers (1995), and the Expository Writing Award of the Institute of Operations Research and Management Science (1999). He is a Fellow of the Institute of Electrical and Electronic Engineers (since 1975).

Yinyu Ye is currently the Kwoh-Ting Li Professor in the School of Engineering at the Department of Management Science and Engineering and Institute of Computational and Mathematical Engineering and the Director of the MS&E Industrial Affiliates Program, Stanford University. He received the B.S. degree in System Engineering from the Huazhong University of Science and Technology, China, and the M.S. and Ph.D. degrees in Engineering-Economic Systems and Operations Research from Stanford University.

Ye's research interests lie in the areas of optimization, complexity theory, algorithm design and analysis, and applications of mathematical programming, operations research and system engineering. He is also interested in developing optimization software for various real-world applications. Current research topics include Liner Programming Algorithms, Markov Decision Processes, Computational Game/Market Equilibrium, Metric Distance Geometry, Dynamic Resource Allocation, and Stochastic and Robust Decision Making, etc. He is an INFORMS (The Institute for Operations Research and The Management Science) Fellow, and has received several research awards including the inaugural 2012ISMP Tseng Lectureship Prize for outstanding contribution to continuous optimization, the 2009John von Neumann Theory Prize for fundamental sustained contributions to theory in Operations Research and the Management Sciences, the inaugural 2006Farkas prize on Optimization, and the 2009 IBM Faculty Award.