Summary: Complete vehicle energy management (CVEM) aims at minimizing the energy consumption of all subsystems inside a vehicle. When the subsystems consist of energy buffers with linear dynamics and/or power converters with quadratic power losses, the CVEM becomes a large-scale and ill-conditioned optimal control problem for which well-known solution approaches (e.g. Pontryagin’s maximum principle, dynamic programming, convex and derivative-free optimization methods) are not effective. In this paper, we design an efficient solution algorithm for this problem by leveraging the framework of operator splitting methods. To facilitate its implementation, we propose a spectral method that automatically tunes the step sizes at every iteration and, in practice, accelerates convergence. Finally, we consider a case study for a parallel-hybrid vehicle and we illustrate the numerical performance of our method by showing that we can efficiently solve a CVEM problem with very large horizons.