  Based on a preconditioned version of the randomized block-coordinate
forward-backward algorithm recently proposed in [Combettes,Pesquet,2014],
several variants of block-coordinate primal-dual algorithms are designed in
order to solve a wide array of monotone inclusion problems. These methods rely
on a sweep of blocks of variables which are activated at each iteration
according to a random rule, and they allow stochastic errors in the evaluation
of the involved operators. Then, this framework is employed to derive
block-coordinate primal-dual proximal algorithms for solving composite convex
variational problems. The resulting algorithm implementations may be useful for
reducing computational complexity and memory requirements. Furthermore, we show
that the proposed approach can be used to develop novel asynchronous
distributed primal-dual algorithms in a multi-agent context.
