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We consider the primal problem of finding the zeros of the sum of a maximallymonotone operator with the composition of another maximally monotone operatorwith a linear continuous operator and a corresponding dual problem formulatedby means of the inverse operators. A primal-dual splitting algorithm whichsimultaneously solves the two problems in finite-dimensional spaces ispresented. The scheme uses at each iteration separately the resolvents of themaximally monotone operators involved and it gives rise to a splittingalgorithm for finding the zeros of the sum of compositions of maximallymonotone operators with linear continuous operators. The iterative schemes areused for solving nondifferentiable convex optimization problems arising inimage processing and in location theory.

A primal-dual splitting algorithm for finding zeros of sums of maximally monotone operators