Overview
- Analyzes the numerical minimization of an objective function
- Broadens understanding of solution algorithms for optimization problems
- Develops and investigates multiset-mappings
- Provides a useful resource for those working to develop solution algorithms
Part of the book series: SpringerBriefs in Optimization (BRIEFSOPTI)
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Table of contents (5 chapters)
Keywords
- numerical minimization of an objective function
- multiset-mappings
- iteration mapping
- numerical variational analysis
- continuity and differentiability of multiset-mappings,
- fixed-point theorem for iteration mappings
- equilibria in dynamical systems
- stability and asymptotic stability for attractors
- dynamical systems
- basin entropy
About this book
Numerical minimization of an objective function is analyzed in this book to understand solution algorithms for optimization problems. Multiset-mappings are introduced to engineer numerical minimization as a repeated application of an iteration mapping. Ideas from numerical variational analysis are extended to define and explore notions of continuity and differentiability of multiset-mappings, and prove a fixed-point theorem for iteration mappings. Concepts from dynamical systems are utilized to develop notions of basin size and basin entropy. Simulations to estimate basins of attraction, to measure and classify basin size, and to compute basin are included to shed new light on convergence behavior in numerical minimization.
Graduate students, researchers, and practitioners in optimization and mathematics who work theoretically to develop solution algorithms will find this book a useful resource.
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Authors and Affiliations
Bibliographic Information
Book Title: Attraction in Numerical Minimization
Book Subtitle: Iteration Mappings, Attractors, and Basins of Attraction
Authors: Adam B. Levy
Series Title: SpringerBriefs in Optimization
DOI: https://doi.org/10.1007/978-3-030-04049-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s), under exclusive licence to Springer Nature Switzerland AG 2018
Softcover ISBN: 978-3-030-04048-2Published: 19 December 2018
eBook ISBN: 978-3-030-04049-9Published: 07 December 2018
Series ISSN: 2190-8354
Series E-ISSN: 2191-575X
Edition Number: 1
Number of Pages: XII, 78
Number of Illustrations: 49 illustrations in colour
Topics: Optimization, Numerical Analysis, Dynamical Systems and Ergodic Theory, Functional Analysis