  In this paper we provide a splitting method for finding a zero of the sum of
a maximally monotone operator, a lipschitzian monotone operator, and a normal
cone to a closed vectorial subspace of a real Hilbert space. The problem is
characterized by a simpler monotone inclusion involving only two operators: the
partial inverse of the maximally monotone operator with respect to the
vectorial subspace and a suitable lipschitzian monotone operator. By applying
the Tseng's method in this context we obtain a splitting algorithm that
exploits the whole structure of the original problem and generalizes partial
inverse and Tseng's methods. Connections with other methods available in the
literature and applications to inclusions involving $m$ maximally monotone
operators, to primal-dual composite monotone inclusions, and to zero-sum games
are provided.

Optimization and Control