Hybrid vehicle energy management can be formulated as an optimal control problem. Considering that the fuel consumption is often computed using linear interpolation over lookup table data, a rigorous analysis of the necessary conditions provided by the Pontryagin Minimum Principle is conducted. For most the co-state values, the control value is well defined and can be computed without any interpolation but this only generate a finite set of state trajectory. To compute the remaining trajectories, it is necessary to consider specific co-state values that generate singular controls. An algorithm is provided for the optimization of both the APU power and binary state and an infinite number of optimal solutions can be constructed.