Abstract:

In this paper we propose an approach for solving convex quadratic programs (QPs) with linear equalities and general linear inequalities by the alternating direction method of multipliers (ADMM). ADMM has attracted considerable interest in recent years in different application fields, especially due to the simplicity of the iteration. We focus on the application of ADMM to the QPs that are solved in Model Predictive Control (MPC) algorithms, where the inequalities represent limits on the states and controls. After introducing our ADMM iteration, we provide a proof of convergence based on the theory of maximal monotone operators. The proving approach allows us to identify a more general measure to monitor the rate of convergence than those previously used and to characterize the optimal step size for the ADMM iterations for the considered class of QPs. While the mathematical result has a similar structure to previous contributions, it allows us to relax some of the previously required assumptions that currently limit the applicability to the QP of model predictive control. The results are validated through numerical simulations on a large number of publicly available QPs, which are generated from an MPC for controlling of a four tank process.