  This work presents an explicit-implicit procedure to compute a model
predictive control (MPC) law with guarantees on recursive feasibility and
asymptotic stability. The approach combines an offline-trained fully-connected
neural network with an online primal active set solver. The neural network
provides a control input initialization while the primal active set method
ensures recursive feasibility and asymptotic stability. The neural network is
trained with a primal-dual loss function, aiming to generate control sequences
that are primal feasible and meet a desired level of suboptimality. Since the
neural network alone does not guarantee constraint satisfaction, its output is
used to warm start the primal active set method online. We demonstrate that
this approach scales to large problems with thousands of optimization
variables, which are challenging for current approaches. Our method achieves a
2x reduction in online inference time compared to the best method in a
benchmark suite of different solver and initialization strategies.
