Overview
- Analyzes an innovative unifying framework for a wide variety of numerical methods? in optimization
- Inspires new convergence analyses for existing methods in numerical optimization?
- Extends and broadens the traditional convergence analyses
Part of the book series: SpringerBriefs in Optimization (BRIEFSOPTI)
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About this book
Stationarity and Convergence in Reduce-or-Retreat Minimization presents and analyzes a unifying framework for a wide variety of numerical methods in optimization. The author’s “reduce-or-retreat” framework is a conceptual method-outline that covers any method whose iterations choose between reducing the objective in some way at a trial point, or retreating to a closer set of trial points. The alignment of various derivative-based methods within the same framework encourages the construction of new methods, and inspires new theoretical developments as companions to results from across traditional divides. The text illustrates the former by developing two generalizations of classic derivative-based methods which accommodate non-smooth objectives, and the latter by analyzing these two methods in detail along with a pattern-search method and the famous Nelder-Mead method.In addition to providing a bridge for theory through the “reduce-or-retreat” framework, this monograph extends and broadens the traditional convergence analyses in several ways. Levy develops a generalized notion of approaching stationarity which applies to non-smooth objectives, and explores the roles of the descent and non-degeneracy conditions in establishing this property. The traditional analysis is broadened by considering “situational” convergence of different elements computed at each iteration of a reduce-or-retreat method. The “reduce-or-retreat” framework described in this text covers specialized minimization methods, some general methods for minimization and a direct search method, while providing convergence analysis which complements and expands existing results.
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Table of contents (3 chapters)
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Front Matter
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Back Matter
Authors and Affiliations
Bibliographic Information
Book Title: Stationarity and Convergence in Reduce-or-Retreat Minimization
Authors: Adam B. Levy
Series Title: SpringerBriefs in Optimization
DOI: https://doi.org/10.1007/978-1-4614-4642-2
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Adam B. Levy 2012
Softcover ISBN: 978-1-4614-4641-5Published: 11 August 2012
eBook ISBN: 978-1-4614-4642-2Published: 10 August 2012
Series ISSN: 2190-8354
Series E-ISSN: 2191-575X
Edition Number: 1
Number of Pages: XII, 55
Number of Illustrations: 2 b/w illustrations, 1 illustrations in colour
Topics: Algorithms, Optimization, Computational Mathematics and Numerical Analysis, Probability Theory and Stochastic Processes, Calculus of Variations and Optimal Control; Optimization