Attraction in Numerical Minimization
Springer International Publishing (Verlag)
978-3-030-04048-2 (ISBN)
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.
1. Multisets and Multiset Mappings.- 2. Iteration Mappings.- 3. Equilibria in Dynamical Systems.- 4. Attractors.- 5. Basin Analysis Via Simulation.
"This book is aimed at researchers and practitioners working in the area of numerical minimization." (Olga Brezhneva, Mathematical Reviews, January, 2020)
“This book is aimed at researchers and practitioners working in the area of numerical minimization.” (Olga Brezhneva, Mathematical Reviews, January, 2020)
| Erscheinungsdatum | 29.12.2018 |
|---|---|
| Reihe/Serie | SpringerBriefs in Optimization |
| Zusatzinfo | XII, 78 p. 49 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 153 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| Schlagworte | basin entropy • continuity and differentiability of multiset-mappi • continuity and differentiability of multiset-mappings, • Dynamical Systems • equilibria in dynamical systems • fixed-point theorem for iteration mappings • iteration mapping • multiset-mappings • numerical minimization of an objective function • numerical variational analysis • stability and asymptotic stability for attractors |
| ISBN-10 | 3-030-04048-8 / 3030040488 |
| ISBN-13 | 978-3-030-04048-2 / 9783030040482 |
| Zustand | Neuware |
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