Complexity Certification of the Fast Alternating Minimization Algorithm for Linear MPC

In this technical note, the fast alternating minimization algorithm (FAMA) is proposed to solve model predictive control (MPC) problems with polytopic and second-order cone constraints. Two splitting strategies with efficient implementations for MPC problems are presented. We derive computational complexity certificates for both splitting strategies, by providing complexity upper-bounds on the number of iterations required to provide a certain accuracy of the dual function value and, most importantly, of the primal solution. This is of particular relevance in the context of real-time MPC in order to bound the required on-line computation time. We further address the computation of the complexity bounds, requiring the solution of a non-convex minimization problem. Finally, we demonstrate the performance of FAMA compared to other splitting methods using a quadrotor example.