Computational unconstrained nonlinear optimization comes to life from a study of the interplay between the metric-based (Cauchy) and model-based (Newton) points of view. The motivating problem is that of minimizing a convex quadratic function. This research monograph reveals for the first time the essential unity of the subject. It explores the relationships between the main methods, develops the Newton-Cauchy framework and points out its rich wealth of algorithmic implications and basic conceptual methods. The monograph also makes a valueable contribution to unifying the notation and terminology of the subject. It is addressed topractitioners, researchers, instructors, and students and provides a useful and refreshing new perspective on computational nonlinear optimization.

Bibliographic Information

Book Title: The Newton-Cauchy Framework
Book Subtitle: A Unified Approach to Unconstrained Nonlinear Minimization
Editors: J. L. Nazareth
Series Title: Lecture Notes in Computer Science
DOI: https://doi.org/10.1007/3-540-57671-1
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1994
Softcover ISBN: 978-3-540-57671-6Published: 28 February 1994
eBook ISBN: 978-3-540-48310-6Published: 01 July 2005
Series ISSN: 0302-9743
Series E-ISSN: 1611-3349
Edition Number: 1
Number of Pages: XII, 108
Topics: Mathematics of Computing, Computer-Aided Engineering (CAD, CAE) and Design, Numerical Analysis, IT in Business, Complexity, Systems Theory, Control

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The Newton-Cauchy Framework

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Table of contents (6 chapters)

Front Matter

Motivation

The metric-based Cauchy perspective

The model-based Newton perspective

The Newton-Cauchy framework

Convergent implementable algorithms

Unconstrained optimization technology

Back Matter

Keywords

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