A Parallel Active-Set Strategy to Solve Sparse Parametric Quadratic Programs arising in MPC

Many different approaches have been proposed for the efficient solution of quadratic programming (QP) problems arising in both linear and nonlinear model predictive control (MPC). This paper presents a novel online QP algorithm that aims at combining the respective advantages of existing methods. It allows for efficient hot-starts of the QP solution and exploits the parametric nature of the problem like other active-set methods. Moreover, like interior-point or fast gradient methods, it directly exploits the inherent sparsity of QP problems arising in MPC and is designed to be easily parallelizable. The proposed parallel active-set strategy is described in detail for MPC problems with diagonal weighting matrices that are subject to state and control bounds; also an extension to the general case is sketched. Numerical properties of the proposed algorithm are discussed and preliminary numerical results are given that are based on a prototype Matlab implementation.