SpringerBriefs in Optimization

Attraction in Numerical Minimization

Iteration Mappings, Attractors, and Basins of Attraction

Authors: Levy, Adam B.

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  • 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
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eBook $54.99
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  • ISBN 978-3-030-04049-9
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Softcover $69.99
price for USA in USD
  • ISBN 978-3-030-04048-2
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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.

Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook $54.99
price for USA in USD (gross)
  • ISBN 978-3-030-04049-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA in USD
  • ISBN 978-3-030-04048-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Attraction in Numerical Minimization
Book Subtitle
Iteration Mappings, Attractors, and Basins of Attraction
Authors
Series Title
SpringerBriefs in Optimization
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
The Author(s), under exclusive licence to Springer Nature Switzerland AG
eBook ISBN
978-3-030-04049-9
DOI
10.1007/978-3-030-04049-9
Softcover ISBN
978-3-030-04048-2
Series ISSN
2190-8354
Edition Number
1
Number of Pages
XII, 78
Number of Illustrations
49 illustrations in colour
Topics