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Attraction in numerical minimization: iteration mappings, attractors, and basins of attraction

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 e...

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Detalles Bibliográficos
Autor principal: Levy, Adam B
Lenguaje:eng
Publicado: Springer 2018
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-030-04049-9
http://cds.cern.ch/record/2650853
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author Levy, Adam B
author_facet Levy, Adam B
author_sort Levy, Adam B
collection CERN
description 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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institution Organización Europea para la Investigación Nuclear
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spelling cern-26508532021-04-21T18:38:49Zdoi:10.1007/978-3-030-04049-9http://cds.cern.ch/record/2650853engLevy, Adam BAttraction in numerical minimization: iteration mappings, attractors, and basins of attractionMathematical Physics and MathematicsNumerical 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.Springeroai:cds.cern.ch:26508532018
spellingShingle Mathematical Physics and Mathematics
Levy, Adam B
Attraction in numerical minimization: iteration mappings, attractors, and basins of attraction
title Attraction in numerical minimization: iteration mappings, attractors, and basins of attraction
title_full Attraction in numerical minimization: iteration mappings, attractors, and basins of attraction
title_fullStr Attraction in numerical minimization: iteration mappings, attractors, and basins of attraction
title_full_unstemmed Attraction in numerical minimization: iteration mappings, attractors, and basins of attraction
title_short Attraction in numerical minimization: iteration mappings, attractors, and basins of attraction
title_sort attraction in numerical minimization: iteration mappings, attractors, and basins of attraction
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-030-04049-9
http://cds.cern.ch/record/2650853
work_keys_str_mv AT levyadamb attractioninnumericalminimizationiterationmappingsattractorsandbasinsofattraction