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...