Mathematical Programming

, Volume 83, Issue 1–3, pp 113–123 | Cite as

Approximate iterations in Bregman-function-based proximal algorithms

  • Jonathan Eckstein
Article

Abstract

This paper establishes convergence of generalized Bregman-function-based proximal point algorithms when the iterates are computed only approximately. The problem being solved is modeled as a general maximal monotone operator, and need not reduce to minimization of a function. The accuracy conditions on the iterates resemble those required for the classical “linear” proximal point algorithm, but are slightly stronger; they should be easier to verify or enforce in practice than conditions given in earlier analyses of approximate generalized proximal methods. Subjects to these practically enforceable accuracy restrictions, convergence is obtained under the same conditions currently established for exact Bregman-function-based proximal methods.

Keywords

Proximal algorithms Bregman functions Monotone operators 

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Copyright information

© The Mathematical Programming Society, Inc 1998

Authors and Affiliations

  • Jonathan Eckstein
    • 1
  1. 1.Faculty of Management and RUTCORRutgers UniversityPiscatawayUSA

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