The Newton-Cauchy Framework [electronic resource] : A Unified Approach to Unconstrained Nonlinear Minimization / edited by J. L. Nazareth.

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

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.