An overview of the dramatic reorganization in reaction to N. Karmakar's seminal 1984 paper on algorithmic linear programming in the area of algorithmic differentiable optimization and equation-solving, or, more simply, algorithmic differentiable programming. Aimed at readers familiar with advanced calculus and numerical analysis.
The Karmarkar Revolution The Newton-Cauchy Method Euler-Newton and Lagrange-NC Methods A Misleading Paradigm CG and the Line Search Gilding the Nelder-Mead Lily Historic Parallels LP from the Newton-Cauchy Perspective Diagonal Metrics and the QC Method LP from the Euler-Newton Perspective Log-Barrier Transformations Karmarkar Potentials and Algorithms Algorithmic Principles Multialgorithms: A New Paradigm An Emerging Discipline Bibliography Index
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)
The Karmarkar Revolution * The Newton-Cauchy Method * Euler-Newton and Lagrange-NC Methods * A Misleading Paradigm * CG and the Line Search * Gilding the Nelder-Mead Lily * Historic Parallels * LP from the Newton-Cauchy Perspective * Diagonal Metrics and the QC Method * LP from the Euler-Newton Perspective * Log-Barrier Transformations * Karmarkar Potentials and Algorithms * Algorithmic Principles * Multialgorithms: A New Paradigm * An Emerging Discipline * Bibliography * Index
This book gives an overview of the dramatic reorganization that has occurred during the last decade in one area of mathematical programming and numerical computation: algorithmic differentiable optimization and equation-solving, or, more simply, algorithmic differentiable programming. The reader is assumed to be familiar with advanced calculus, numerical analysis, the theory and algorithms of linear and nonlinear programming, and the fundamentals of computer science. Thus, this monograph is intended for researchers in optimization and advanced graduate students. But others will find the ideas to be of interest as well.