Mathematical Programming

, Volume 83, Issue 1–3, pp 113–123

Approximate iterations in Bregman-function-based proximal algorithms

  • Jonathan Eckstein

DOI: 10.1007/BF02680553

Cite this article as:
Eckstein, J. Mathematical Programming (1998) 83: 113. doi:10.1007/BF02680553


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.


Proximal algorithms Bregman functions Monotone operators 

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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