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A parallel splitting method is proposed for solving systems of coupledmonotone inclusions in Hilbert spaces. Convergence is established for a wideclass of coupling schemes. Unlike classical alternating algorithms, which arelimited to two variables and linear coupling, our parallel method can handle anarbitrary number of variables as well as nonlinear coupling schemes. Thebreadth and flexibility of the proposed framework is illustrated throughapplications in the areas of evolution inclusions, dynamical games, signalrecovery, image decomposition, best approximation, network flows, andvariational problems in Sobolev spaces.

A parallel splitting method for weakly coupled monotone inclusions