Linear and Nonlinear Programming

by David G. Luenberger, Yinyu Ye

Overview

"Linear and Nonlinear Programming" is considered a classic textbook in Optimization. While it is a classic, it also reflects modern theoretical insights. These insights provide structure to what might otherwise be simply a collection of techniques and results, and this is valuable both as a means for learning existing material and for developing new results. One major insight of this type is the connection between the purely analytical character of an optimization problem, expressed perhaps by properties of the necessary conditions, and the behavior of algorithms used to solve a problem. This was a major theme of the first and second editions. Now the third edition has been completely updated with recent Optimization Methods. The new co-author, Yinyu Ye, has written chapters and chapter material on a number of these areas including Interior Point Methods.

Product Details

ISBN-13:	9781441945044
Publisher:	Springer US
Publication date:	11/19/2010
Series:	International Series in Operations Research & Management Science , #116
Edition description:	Softcover reprint of hardcover 3rd ed. 2008
Pages:	546
Product dimensions:	6.10(w) x 9.10(h) x 1.20(d)

About the Author

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

He is a Member of the National Academy of Engineering (2008) and has received e.g. 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. He received his B.S. degree in System Engineering from Huazhong University of Science and Technology, China, and his M.S. and Ph.D. degrees in Engineering-Economic Systems and Operations Research from Stanford University. He is an INFORMS (The Institute for Operations Research and The Management Science). Fellow since 2012, and has received several academic awards including: the 2009 John von Neumann Theory Prize for fundamental sustained contributions to theory in Operations Research and the Management Sciences, the 2015 SPS Signal Processing Magazine Best Paper Award, the winner of the 2014 SIAM Optimization Prize awarded (every three years), the inaugural 2012 ISMP Tseng Lectureship Prize for outstanding contribution to continuous optimization (every three years), the inaugural 2006 Farkas Prize on Optimization, the 2009 IBM Faculty Award.

Table of Contents

Linear Programming.- Basic Properties of Linear Programs.- The Simplex Method.- Duality.- Interior-Point Methods.- Transportation and Network Flow Problems.- Unconstrained Problems.- Basic Properties of Solutions and Algorithms.- Basic Descent Methods.- Conjugate Direction Methods.- Quasi-Newton Methods.- Constrained Minimization.- Constrained Minimization Conditions.- Primal Methods.- Penalty and Barrier Methods.- Dual and Cutting Plane Methods.- Primal-Dual Methods.

What People are Saying About This

A reader from Greece

I have the 1977 edition from my father's MIT days. I am a Mathematician and I can verify that the book written in 1977 is of the same style that good books have today. A book is not made obsolete because some new "elegant" terms arise.

Giorgio Azvaris

I have profitably used the book to apply constrained minimization procedures in the field of computational contact mechanics. I think it is not a secret that quite often books on mathematics are written from mathematicians for mathematicians. Hence it is quite hard for engineers to read and to extract valuable information from them. With this respect this book is a shining star. It presents the topics in a very precise but clear and understandable way. (Turin, Italy)

Editorial Reviews

From the reviews of the third edition:

“The aim of this book is to present the central concepts of optimization techniques. … the material in this new edition is organized into three separate parts. … 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)

From the Publisher