Alternating direction method of multipliers for strictly convex quadratic programs: Optimal parameter selection

We consider an approach for solving strictly convex quadratic programs (QPs) with general linear inequalities by the alternating direction method of multipliers (ADMM). In particular, we focus on the application of ADMM to the QPs of constrained Model Predictive Control (MPC). After introducing our ADMM iteration, we provide a proof of convergence closely related to the theory of maximal monotone operators. The proof relies on a general measure to monitor the rate of convergence and hence to characterize the optimal step size for the iterations. We show that the identified measure converges at a Q-linear rate while the iterates converge at a 2-step Q-linear rate. This result allows us to relax some of the existing assumptions in optimal step size selection, that currently limit the applicability to the QPs of MPC. The results are validated through a large public benchmark set of QPs of MPC for controlling a four tank process.