  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.
