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Convex optimization has recently been suggested for solving the optimal energy management problem of hybrid electric vehicles. Compared with dynamic programming, this approach can significantly reduce the computational time, but the price to pay is additional model approximations and heuristics for discrete decision variables such as engine on/off control. In this paper, the globally optimal engine on/off conditions are derived analytically. It is demonstrated that the optimal engine on/off strategy is to switch the engine on if and only if the requested power exceeds a certain nonconstant threshold. By iteratively computing the threshold and the power split using convex optimization, the optimal solution to the energy management problem is found. The effectiveness of the presented approach is demonstrated in two sizing case studies. The first case study deals with high-energy-capacity batteries, whereas the …