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