Fast Coordinate Descent Augmented Lagrangian Methods for linearized MPC

Abstract

This paper proposes Coordinate Descent Augmented Lagrangian based methods for solving linear and nonlinear Model Predictive Control (MPC) problems. The augmented Lagrangian relaxation to handle the equality constraints over the dynamics of the systems is used and dual accelerated gradient method based on inexact dual gradient information for solving the corresponding dual problem is applied. Then, three algorithms that solve the inner subproblem that arises from minimizing the Augmented Lagrangian are presented: the coordinate descent method, the accelerated proximal coordinate descent method and the restarted accelerated coordinate descent method. A detailed comparison between these methods is provided on several test cases.