Multilevel parallel GPU implementation of SQP solvers for Nonlinear MPC

In recent literature, it has been shown that the number of steps in a sequential quadratic programming algorithm for a non-linear model predictive control (NMPC) problem can be greatly reduced by a parallel shooting method. The efficiency of such a parallel shooting method further depends on how the algorithm is implemented on parallel computing platforms such as Graphics Processing Units (GPUs). The GPU implementation should consider the degree of parallelism necessary for higher time efficiency as well as the hardware resource consumption/limitation at the GPU for a given problem size. In this paper, we present a multilevel parallel GPU implementation for sequential quadratic programming and an (Alternating Direction Method of Multipliers) ADMM solver. First, we introduce a GPU implementation enabling parallel computing of many quadratic programs (QPs) by functional parallelism. Next, we parallelize each QP solver using data parallelism of basic linear matrix operations. We show that the proposed GPU implementation greatly scales with the degree of parallelism in the parallel shooting method. Further, we show how a GPU implementation can be configured for a given problem size avoiding resource overprovisioning.