  In this work we study a constrained monotone inclusion involving the normal
cone to a closed vector subspace and a priori information on primal solutions.
We model this information by imposing that solutions belongs to the fixed point
set of an averaged nonexpansive mapping. We characterize the solutions using an
auxiliary inclusion that involves the partial inverse operator. Then, we
propose the primal-dual partial inverse splitting and we prove its weak
convergence to a solution of the inclusion, generalizing several methods in the
literature. The efficiency of the proposed method is illustrated in two
non-smooth convex optimization problems whose constraints have vector subspace
structure. Finally, the proposed algorithm is applied to find a solution to a
stochastic arc capacity expansion problem in transport networks.
