Buch, Englisch, 78 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 154 g
Iteration Mappings, Attractors, and Basins of Attraction
Buch, Englisch, 78 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 154 g
Reihe: SpringerBriefs in Optimization
ISBN: 978-3-030-04048-2
Verlag: Springer International Publishing
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.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Optimierung
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
- Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
Weitere Infos & Material
1. Multisets and Multiset Mappings.- 2. Iteration Mappings.- 3. Equilibria in Dynamical Systems.- 4. Attractors.- 5. Basin Analysis Via Simulation.
