The Newton-Cauchy Framework

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.