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    Attraction in Numerical Minimization

Attraction in Numerical Minimization

Adam B. Levy
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      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.
      Format: Paperback / softback CONTRIBUTORS: Adam B. Levy EAN: 9783030040482 COUNTRY: Switzerland PAGES: WEIGHT: 454 g HEIGHT: 235 cm
      PUBLISHED BY: Springer Nature Switzerland AG DATE PUBLISHED: 2018-12-19 CITY: GENRE: MATHEMATICS / Applied, MATHEMATICS / Number Systems, MATHEMATICS / Mathematical Analysis, MATHEMATICS / Functional Analysis WIDTH: 155 cm SPINE:

      Book Themes:

      Cybernetics and systems theory, Functional analysis and transforms, Numerical analysis, Optimization

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      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.
      Format: Paperback / softback CONTRIBUTORS: Adam B. Levy EAN: 9783030040482 COUNTRY: Switzerland PAGES: WEIGHT: 454 g HEIGHT: 235 cm
      PUBLISHED BY: Springer Nature Switzerland AG DATE PUBLISHED: 2018-12-19 CITY: GENRE: MATHEMATICS / Applied, MATHEMATICS / Number Systems, MATHEMATICS / Mathematical Analysis, MATHEMATICS / Functional Analysis WIDTH: 155 cm SPINE:

      Book Themes:

      Cybernetics and systems theory, Functional analysis and transforms, Numerical analysis, Optimization

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