  In this paper we propose a parallel coordinate descent algorithm for solving
smooth convex optimization problems with separable constraints that may arise
e.g. in distributed model predictive control (MPC) for linear network systems.
Our algorithm is based on block coordinate descent updates in parallel and has
a very simple iteration. We prove (sub)linear rate of convergence for the new
algorithm under standard assumptions for smooth convex optimization. Further,
our algorithm uses local information and thus is suitable for distributed
implementations. Moreover, it has low iteration complexity, which makes it
appropriate for embedded control. An MPC scheme based on this new parallel
algorithm is derived, for which every subsystem in the network can compute
feasible and stabilizing control inputs using distributed and cheap
computations. For ensuring stability of the MPC scheme, we use a terminal cost
formulation derived from a distributed synthesis. Preliminary numerical tests
show better performance for our optimization algorithm than other existing
methods.
