Proximal Decomposition on the Graph of a Maximal Monotone Operator

We present an algorithm to solve: Find $( x,y ) \in A \times A^ \bot $ such that $y \in Tx$, where $A$ is a subspace and $T$ is a maximal monotone operator. The algorithm is based on the proximal decomposition on the graph of a monotone operator and we show how to recover Spingarn's decompositi...

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Bibliographic Details
Published in:SIAM journal on optimization 1995-05, Vol.5 (2), p.454-466
Main Authors: Mahey, Philippe, Oualibouch, Said, Tao, Pham Dinh
Format: Article
Language:English
Subjects:
Algorithms
Decomposition
Mathematics
Optimization
Optimization and Control
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Summary:We present an algorithm to solve: Find $( x,y ) \in A \times A^ \bot $ such that $y \in Tx$, where $A$ is a subspace and $T$ is a maximal monotone operator. The algorithm is based on the proximal decomposition on the graph of a monotone operator and we show how to recover Spingarn's decomposition method. We give a proof of convergence that does not use the concept of partial inverse and show how to choose a scaling factor to accelerate the convergence in the strongly monotone case. Numerical results performed on quadratic problems confirm the robust behaviour of the algorithm.
ISSN:1052-6234
1095-7189
DOI:10.1137/0805023