Differentiable Optimization and Equation Solving
A Treatise on Algorithmic Science and the Karmarkar Revolution
Authors: Nazareth, John
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- About this book
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In 1984, N. Karmarkar published a seminal paper on algorithmic linear programming. During the subsequent decade, it stimulated a huge outpouring of new algorithmic results by researchers world-wide in many areas of mathematical programming and numerical computation. This book gives an overview of the resulting, dramatic reorganization that has occurred in one of these areas: algorithmic differentiable optimization and equation-solving, or, more simply, algorithmic differentiable programming. The book is aimed at readers familiar with advanced calculus, numerical analysis, in particular numerical linear algebra, the theory and algorithms of linear and nonlinear programming, and the fundamentals of computer science, in particular, computer programming and the basic models of computation and complexity theory.
"Very fine monograph...filled with great insights."
-Joseph F. Traub, Columbia University
- Reviews
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From the reviews:
...beautifully done, well organized, and a valuable reference book on the subject.
- George Dantzig, Stanford University
Nazareth has written an excellent book that includes both introductory and advanced topics. It provides a description of many of the techniques in this area. In addition, the book is sprinkled with beautiful analogies and insights. These insights make this book an interesting read and a learning experience for both the novice and the expert.
- Henry Wolkowicz, Notes of the Canadian Mathematical Society
“This monograph brings together research that was published by the author in several journal papers. It tells an intriguing story of the mechanism that unifies and differentiates between the multitude of algorithms that were developed in the pre and post Karmarkar period. The reader is supposed to be familiar with advanced calculus, numerical analysis, and computer science. … it is aiming at researchers and advanced students. The text is written with the greatest care, a scholar example op clear mathematical writing.” (Adhemar Bultheel, Bulletin of the Belgian Mathematical Society, 2007)
- Table of contents (15 chapters)
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The Karmarkar Revolution
Pages 3-10
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The Newton-Cauchy Method
Pages 11-24
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Euler-Newton and Lagrange-NC Methods
Pages 25-45
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A Misleading Paradigm
Pages 49-55
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CG and the Line Search
Pages 57-72
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Table of contents (15 chapters)
- Download Preface 1 PDF (55 KB)
- Download Sample pages 1 PDF (112.7 KB)
- Download Sample pages 0 PDF (322.3 KB)
- Download Table of contents PDF (60.9 KB)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Differentiable Optimization and Equation Solving
- Book Subtitle
- A Treatise on Algorithmic Science and the Karmarkar Revolution
- Authors
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- John Nazareth
- Series Title
- CMS Books in Mathematics
- Copyright
- 2003
- Publisher
- Springer-Verlag New York
- Copyright Holder
- John Lawrence Nazareth
- eBook ISBN
- 978-0-387-21788-8
- DOI
- 10.1007/b97521
- Hardcover ISBN
- 978-0-387-95572-8
- Softcover ISBN
- 978-1-4419-3061-3
- Series ISSN
- 1613-5237
- Edition Number
- 1
- Number of Pages
- XVII, 256
- Number of Illustrations
- 2 b/w illustrations
- Topics
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