Differentiable Optimization and Equation Solving: A Treatise on Algorithmic Science and the Karmarkar Revolution

ISBN-13: 9781441930613 / Angielski / Miękka / 2011 / 256 str.

John L. Nazareth

Opis

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. J.L. Nazareth is a Professor in the Department of Pure and Applied Mathematics at Washington State University. He is the author of two books previously published by Springer-Verlag, DLP and Extensions: An Optimization Model and Decision Support System (2001) and The Newton-Cauchy Framework: A Unified Approach to Unconstrained Nonlinear Minimization (1994).

Recenzje

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)

Spis treści

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