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A Gradient-Type Method and Applications

  • Antonio André Novotny
  • Jan Sokołowski
  • Antoni Żochowski
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 188)

Abstract

In classical optimization the first family of numerical methods is based on the linear approximation of the functional to be minimized. The same idea is used in the topological derivative method. The functional is approximated by the first order expansion with respect to the small parameter. The parameter governs the size of singular domain perturbation which we call the topological perturbation.

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Antonio André Novotny
    • 1
  • Jan Sokołowski
    • 2
    • 3
    • 4
  • Antoni Żochowski
    • 3
  1. 1.Coordenação de Métodos Matemáticos e ComputacionaisLaboratório Nacional de Computação Científica LNCC/MCTICPetrópolisBrazil
  2. 2.Institut Élie Cartan de Nancy, UMR 7502Université de Lorraine, CNRSVandœuvre-Lès-NancyFrance
  3. 3.Systems Research InstitutePolish Academy of SciencesWarsawPoland
  4. 4.Universidade Federal da Paraiba, Centro de informaticaJoão PessoaBrazil

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