This paper investigates a concept of an electrically supercharged internal combustion engine ( ICE) powertrain. A supercharger consists of an electric motor and a compressor. It draws its power from an electric energy buffer ( e. g., a battery) and helps the engine during short-duration high-power demands. Both the engine and the buffer are sized to reduce the sum of the vehicle operational ( fuel) and component ( engine and buffer) costs. For this purpose, a convex driving cycle-based vehicle model is derived, enabling the formulation of an underlying optimization problemas a second-order cone program ( SOCP). Such a program can be efficiently solved using dedicated numerical tools ( for a given gear selection strategy), which provides not only the optimal engine/buffer sizes but optimal vehicle control and state trajectories ( e. g., compressor power and buffer energy) as well. Finally, the results obtained from a representative numerical case study are discussed in detail.