  In this paper, we propose a numerical approach for solving composite
primal-dual monotone inclusions with a priori information. The underlying a
priori information set is represented by the intersection of fixed point sets
of a finite number of operators, and we propose and algorithm that activates
the corresponding set by following a finite-valued random variable at each
iteration. Our formulation is flexible and includes, for instance,
deterministic and Bernoulli activations over cyclic schemes, and Kaczmarz-type
random activations. The almost sure convergence of the algorithm is obtained by
means of properties of stochastic Quasi-Fej\'er sequences. We also recover
several primal-dual algorithms for monotone inclusions in the context without a
priori information and classical algorithms for solving convex feasibility
problems and linear systems. In the context of convex optimization with
inequality constraints, any selection of the constraints defines the a priori
information set, in which case the operators involved are simply projections
onto half spaces. By incorporating random projections onto a selection of the
constraints to classical primal-dual schemes, we obtain faster algorithms as we
illustrate by means of a numerical application to a stochastic arc capacity
expansion problem in a transport network.
