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

We consider the primal problem of finding the zeros of the sum of a maximally monotone operator with the composition of another maximally monotone operator with a linear continuous operator and a corresponding dual problem formulated by means of the inverse operators. A primal-dual splitting algorithm which simultaneously solves the two problems in finite-dimensional spaces is presented. The scheme uses at each iteration separately the resolvents of the maximally monotone operators involved and it gives rise to a splitting algorithm for finding the zeros of the sum of compositions of maximally monotone operators with linear continuous operators. The iterative schemes are used for solving nondifferentiable convex optimization problems arising in image processing and in location theory.