Engine start-stop system is one of the main mechanisms for fuel saving in hybrid electric vehicles (HEVs). During those transient events, especially during engine starts, the engine torque pulsations can be an NVH issue if there is direct mechanical coupling between the engine and the driveline. In addition, engine starts may also result in the interruption of driving torque. The fast torque response of the electric machines provides a possible solution to mitigate the output torque fluctuation. But the effect is limited by the capability of these two electric machines due to the three missions they must satisfy simultaneously, i.e., starting the engine, compensating the torque pulsations and providing the demanded driving torque. To thoroughly understand this problem and propose possible solutions, in this study, we developed an input-split HEV powertrain model with a grounding clutch. The Dynamic Programming (DP) technique is adopted as the optimization approach to investigate the maximum output torque we can have without any torque error during engine starts. At the same time, the relationship between these two conflicting goals is achieved and the optimal solutions can be divided into four parts depending on the driver demand torque, from the minimum engine start time solution to the maximum driver torque demand solution. Based on the DP results, a control algorithm is proposed to achieve smooth and quick mode transition from the EV mode to power-split driving while meeting the driver torque demand.