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In this paper we propose a parallel coordinate descent algorithm for solvingsmooth convex optimization problems with separable constraints that may arisee.g. in distributed model predictive control (MPC) for linear network systems.Our algorithm is based on block coordinate descent updates in parallel and hasa very simple iteration. We prove (sub)linear rate of convergence for the newalgorithm under standard assumptions for smooth convex optimization. Further,our algorithm uses local information and thus is suitable for distributedimplementations. Moreover, it has low iteration complexity, which makes itappropriate for embedded control. An MPC scheme based on this new parallelalgorithm is derived, for which every subsystem in the network can computefeasible and stabilizing control inputs using distributed and cheapcomputations. For ensuring stability of the MPC scheme, we use a terminal costformulation derived from a distributed synthesis. Preliminary numerical testsshow better performance for our optimization algorithm than other existingmethods.

Efficient parallel coordinate descent algorithm for convex optimization problems with separable constraints: application to distributed MPC