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"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.
List 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.
About the author
David G. Luenberger is a professor in the School of Engineeringat Stanford University. He has published four textbooks and over 70 technical papers. Professor Luenberger is a Fellow of the Institute of Electrical and Electronics Engineers. His current research is mainly in investment science, economics, and planning.
Summary
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.
Additional text
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)
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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)
