The Newton-Cauchy Framework: A Unified Approach to Unconstrained Nonlinear Minimization

J. L. Nazareth (eds.)3540576711, 9783540576716

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.

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Table of contents :
Motivation….Pages 1-25
The metric-based Cauchy perspective….Pages 26-40
The model-based Newton perspective….Pages 41-53
The Newton-Cauchy framework….Pages 54-74
Convergent implementable algorithms….Pages 75-85
Unconstrained optimization technology….Pages 86-90