QPALM-OCP: A Newton-Type Proximal Augmented Lagrangian Solver Tailored for Quadratic Programs Arising in Model Predictive Control

In model predictive control fast and reliable quadratic programming solvers are of fundamental importance. The inherent structure of the subsequent optimal control problems can lead to substantial performance improvements if exploited. Therefore, we present a structure-exploiting solver based on proximal augmented Lagrangian, extending the general-purpose quadratic programming solver QPALM. Our solver relies on semismooth Newton iterations to solve the inner sub-problem while directly accounting for the optimal control problem structure via efficient and sparse matrix factorizations. The matrices to be factorized depend on the active-set and therefore low-rank factorization updates can be employed like in active-set methods resulting in cheap iterates. We compare our solver with QPALM and other well-known solvers and show its benefits in a numerical example.