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A Framework for Analyzing Local Convergence Properties with Applications to Proximal-Point Algorithms

  • Y. D. Dong
  • A. Fischer
Article

Abstract

A general algorithmic scheme for solving inclusions in a Banach space is investigated in respect to its local convergence behavior. Particular emphasis is placed on applications to certain proximal-point-type algorithms in Hilbert spaces. The assumptions do not necessarily require that a solution be isolated. In this way, results existing for the case of a locally unique solution can be extended to cases with nonisolated solutions. Besides the convergence rates for the distance of the iterates to the solution set, strong convergence to a sole solution is shown as well. As one particular application of the framework, an improved convergence rate for an important case of the inexact proximal-point algorithm is derived.

Keywords

Inclusions generalized equations local convergence upper Lipschitz continuity nonisolated solutions proximal-point algorithms 

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Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  • Y. D. Dong
    • 1
  • A. Fischer
    • 2
  1. 1.Department of MathematicsZhengzhou UniversityZhengzhouP.R. China
  2. 2.Institute of Numerical MathematicsTechnische Universität DresdenDresdenGermany

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