Approximate iterations in Bregman-function-based proximal algorithms

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...

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Bibliographic Details
Published inMathematical programming Vol. 83; no. 1-3; pp. 113 - 123
Main Author Eckstein, Jonathan
Format Journal Article
LanguageEnglish
Published Heidelberg Springer 01.09.1998
Springer Nature B.V
Subjects
Algorithms
Applied sciences
Convergence
Exact sciences and technology
Operational research and scientific management
Operational research. Management science
Optimization. Search problems
Monotone operator
Algorithms
Proximal point method
Optimization
Convergence
Bregman function
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Summary: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.
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ISSN:0025-5610
1436-4646
DOI:10.1007/BF02680553