Linear and Nonlinear Programming

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Springer Science & Business Media, Jun 20, 2008 - Business & Economics - 546 pages
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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.  Yinyu Ye has written chapters and chapter material on a number of these areas including Interior Point Methods.

This book is designed for either self-study by professionals or classroom work at the undergraduate or graduate level for technical students. Like the field of optimization itself, which involves many classical disciplines, the book should be useful to system analysts, operations researchers, numerical analysts, management scientists, and other specialists.

 

 

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Contents

Introduction
1
Basic Properties of Linear Programs
11
The Simplex Method
33
Duality
79
InteriorPoint Methods
111
Transportation and Network Flow Problems
145
Basic Properties of Solutions and Algorithms
183
Basic Descent Methods
215
Constrained Minimization Conditions
321
Primal Methods
359
Penalty and Barrier Methods
401
Dual and Cutting Plane Methods
435
PrimalDual Methods
469
Appendix A Mathematical Review
507
Appendix B Convex Sets
515
Gaussian Elimination
523

Conjugate Direction Methods
263
QuasiNewton Methods
285

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About the author (2008)

David G. Luenberger has directed much of his career toward teaching "portable concepts" - organizing theory around concepts and actually "porting" the concepts to applications where, in the process, the general concepts are often discovered. The search for fundamentals has explicitly directed his research in the fields of control, optimization, planning, economics, and investments, and in turn, it is the discovery of these fundamentals that have motivated his textbook writing projects.