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

► We propose a parallel optimization algorithm for solving MPC problems. ► The algorithm is based on coordinate descent updates with low iteration complexity. ► We prove that for strongly convex functions it has linear rate of convergence. ► We show that the algorithm is suitable for embedded contro...

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Vydané v:	Journal of process control Ročník 23; číslo 3; s. 243 - 253
Hlavní autori:	Necoara, Ion, Clipici, Dragos
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier Ltd 01.03.2013
Predmet:	(Sub)linear convergence rate Coordinate descent optimization Distributed model predictive control Embedded control Parallel algorithm Coordinate descent optimization Distributed model predictive control (Sub)linear convergence rate Parallel algorithm Embedded control
ISSN:	0959-1524, 1873-2771
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Popis
Shrnutí:	► We propose a parallel optimization algorithm for solving MPC problems. ► The algorithm is based on coordinate descent updates with low iteration complexity. ► We prove that for strongly convex functions it has linear rate of convergence. ► We show that the algorithm is suitable for embedded control, e.g. PLC. ► We give a distributed synthesis for a terminal cost that ensures stability of MPC. 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.
ISSN:	0959-1524 1873-2771
DOI:	10.1016/j.jprocont.2012.12.012