This paper proposes a design method for the Energy Management Strategy to explore the potential fuel saving of a Hybrid Electric Vehicle equipped with an Automated Manual Transmission. The control algorithm is developed based on the combination of Dynamic Programming and Pontryagins Minimum Principle to optimally control the discrete gear shift command in addition to the continuous power split between the internal combustion engine and the electric machine. The proposed method outperforms Dynamic Programming in terms of computational efficiency with 171 times faster without loss of accuracy. Simulation results for a mid-sized Hybrid Electric Vehicle on the New European Drive Cycle show that by further optimizing the gear shift strategy, an additional fuel saving of 20.3% can be reached. Furthermore, with the start-stop functionality available, it is shown that the two-point boundary value problem following from Pontryagins Minimum Principle can not be solved with sufficient accuracy without loss of optimality. This means that the finding of a constant value for the Lagrange multiplier while satisfying the battery state of energy at the terminal time is not always guaranteed. Therefore an alternative approach of state of energy feedback control to adapt the Lagrange multiplier is adopted. The obtained results are very close to the globally optimal solution from Dynamic Programming. Simulation results, including the start-stop functionality, show the relative fuel saving can be up to 26.8% compared to the case of a standard gear shift strategy.