PROXIMAL DECOMPOSITION ON THE GRAPH OF A MAXIMAL MONOTONE OPERATOR

We present an algorithm to solve: Find (x, y) epsilon A x A perpendicu lar to such that y epsilon Tx, where A is a subspace and T is a maxima l monotone operator. The algorithm is based on the proximal decomposit ion on the graph of a monotone operator and we show how to recover Spi ngarn's decomposition method. We give a proof of convergence that does not use the concept of partial inverse and show how to choose a scali ng factor to accelerate the convergence in the strongly monotone case. Numerical results performed on quadratic problems confirm the robust behaviour of the algorithm.