ADMM Prescaling for Model Predictive Control

The alternating direction method of multipliers (ADMM) is an iterative first order optimization algorithm for solving convex problems such as the ones arising in linear model predictive control (MPC). The ADMM convergence rate depends on a penalty (or step size) parameter that is often difficult to choose. In this paper we present an ADMM prescaling strategy for strongly convex quadratic problems with linear equality and box constraints. We apply this prescaling procedure to MPC-type problems with diagonal objective, which results in an elimination of the penalty parameter. Moreover, we illustrate our results in a numerical study that demonstrates the benefits of prescaling.