A Class of Inexact Variable Metric Proximal Point Algorithms

For the problem of solving maximal monotone inclusions, we present a rather general class of algorithms, which contains hybrid inexact proximal point methods as a special case and allows for the use of a variable metric in subproblems. The global convergence and local linear rate of convergence are...

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Bibliographic Details
Published in:SIAM journal on optimization 2008-01, Vol.19 (1), p.240-260
Main Authors: Parente, L. A., Lotito, P. A., Solodov, M. V.
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Methods
Optimization
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Summary:For the problem of solving maximal monotone inclusions, we present a rather general class of algorithms, which contains hybrid inexact proximal point methods as a special case and allows for the use of a variable metric in subproblems. The global convergence and local linear rate of convergence are established under standard assumptions. We demonstrate the advantage of variable metric implementation in the case of solving systems of smooth monotone equations by the proximal Newton method.
ISSN:1052-6234
1095-7189
DOI:10.1137/070688146