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Optimization pp 83–90Cite as

Relaxed Assumptions for Iteration Methods

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Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 481))

Abstract

We consider a general inexact iterative method for finding a fixed point of a nonexpansive mapping on a real Hilbert space. Proofs of convergence of sequences generated by such a method generally require at least that the error term goes to zero. The aim of the present paper is to weaken this nonrealistic theoretical assumption. The obtained result is applied to the proximal point algorithm.

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References

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Author information

Authors and Affiliations

  1. Institut de Mathématiques, Université de Liège, 4000, Liège, Belgium

    Myrana Brohé & Patricia Tossings

Authors
  1. Myrana Brohé
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  2. Patricia Tossings
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Namur, Rue de Bruxelles 61, 5000, Namur, Belgium

    Van Hien Nguyen  & Jean-Jacques Strodiot  & 

  2. Institut de Mathématiques (B37), University of Liège, Grande Traverse 12, 4000, Liège, Belgium

    Patricia Tossings

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© 2000 Springer-Verlag Berlin Heidelberg

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Brohé, M., Tossings, P. (2000). Relaxed Assumptions for Iteration Methods. In: Nguyen, V.H., Strodiot, JJ., Tossings, P. (eds) Optimization. Lecture Notes in Economics and Mathematical Systems, vol 481. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57014-8_6

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  • DOI: https://doi.org/10.1007/978-3-642-57014-8_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66905-0

  • Online ISBN: 978-3-642-57014-8

  • eBook Packages: Springer Book Archive

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