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

Ion Necoara (ion.necoara***at***acse.pub.ro)
Dragos Clipici (d.clipici***at***acse.pub.ro)

Abstract: 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.

Keywords: Coordinate descent optimization, parallel algorithm, (sub)linear convergence rate, distributed model predictive control, embedded control.

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Optimization Software and Modeling Systems (Parallel Algorithms )

Category 3: Applications -- Science and Engineering (Control Applications )

Citation: Journal of Process Control, pp. 1-26, in print, 2012.

Download: [PDF]

Entry Submitted: 11/02/2012
Entry Accepted: 11/02/2012
Entry Last Modified: 02/13/2013

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