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

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 co...