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Proximal decomposition on the graph of a maximal monotone operator. (English) Zbl 0834.90105
Summary: We present an algorithm to solve: Find (x,y)A×A such that yTx, 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:
90C25Convex programming