The Newton-Cauchy Framework

1. Front Matter

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2. Motivation

   Pages 1-25

3. The metric-based Cauchy perspective

   Pages 26-40

4. The model-based Newton perspective

   Pages 41-53

5. The Newton-Cauchy framework

   Pages 54-74

6. Convergent implementable algorithms

   Pages 75-85

7. Unconstrained optimization technology

   Pages 86-90

8. Back Matter

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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.

• Gradient Method
• Gradientenverfahren
• Mathematical Programming
• Mathematisches Programmieren
• Motivation
• Newton-Cauchy Method
• Newton-Cauchy Verfahren
• Nichtlineare Optimierung
• Unbeschränkte Minimierung
• Unconstrained Minimization
• algorithm
• algorithms
• linear optimization
• nonlinear optimization
• optimization
• complexity

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