© 2018

Attraction in Numerical Minimization

Iteration Mappings, Attractors, and Basins of Attraction

  • 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


Part of the SpringerBriefs in Optimization book series (BRIEFSOPTI)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Adam B. Levy
    Pages 1-10
  3. Adam B. Levy
    Pages 11-22
  4. Adam B. Levy
    Pages 23-31
  5. Adam B. Levy
    Pages 33-42
  6. Adam B. Levy
    Pages 43-75
  7. Back Matter
    Pages 77-78

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.


numerical minimization of an objective function multiset-mappings iteration mapping numerical variational analysis continuity and differentiability of multiset-mappings, fixed-point theorem for iteration mappings equilibria in dynamical systems stability and asymptotic stability for attractors dynamical systems basin entropy

Authors and affiliations

  1. 1.Bowdoin CollegeBrunswickUSA

Bibliographic information

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“This book is aimed at researchers and practitioners working in the area of numerical minimization.” (Olga Brezhneva, Mathematical Reviews, January, 2020)