In the paper we employ numerical optimal control techniques to define the best transient operating strategy for a turbocharger power assist system (TPAS). A TPAS is any device capable of bi-directional energy transfer to the turbocharger shaft and energy storage. When applied to turbocharged diesel engines, the TPAS results in significant reduction of the turbo-lag. The optimum transient strategy is capable of improving the vehicle acceleration performance with no deterioration in smoke emissions. These benefits can be attained even if the net energy contribution by the TPAS during the acceleration interval is zero, i.e., all energy is re-generated and returned back to the energy storage by the end of the acceleration interval. At the same time the total fuel consumption during the acceleration interval may be reduced. These results are compared to the “conventional” vehicle (without TPAS) and to the case when the supplemental energy is applied directly to or taken directly from the crankshaft as in a parallel hybrid vehicle configuration. Comparison with the conventional vehicle and with the parallel hybrid vehicle reveals the mechanism by which TPAS can reduce pumping losses at the initial phase of acceleration thereby improving fuel economy.