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Zbl 0834.90105
Mahey, Philippe; Oualibouch, Said; Pham Dinh Tao
Proximal decomposition on the graph of a maximal monotone operator.
(English)
[J] SIAM J. Optim. 5, No.2, 454-466 (1995). ISSN 1052-6234; ISSN 1095-7189/e

Summary: We present an algorithm to solve: Find $(x, y)\in A\times A^\perp$ 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.
MSC 2000:
*90C25 Convex programming

Keywords: proximal point algorithm; partial inverse; maximal monotone operator

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