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

ISBN-13: 9783540576716 / Angielski / Miękka / 1994 / 108 str.

John L. Nazareth

Opis

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.

Spis treści

Motivation.- The metric-based Cauchy perspective.- The model-based Newton perspective.- The Newton-Cauchy framework.- Convergent implementable algorithms.- Unconstrained optimization technology.