This paper presents HypoEnergy, a framework for extending the hybrid battery-supercapacitor power supply life- time. HypoEnergy combines high energy density and reliable workload supportability of an electrochemical battery with high power density and high number of recharge cycles of supercapacitors. The lifetime optimizations consider nonlinear battery characteristics and supercapacitors’ charging overhead. HypoEnergy-KI studies the hybrid supply lifetime optimization for a preemptively known workload and for one ideal superca- pacitor. We show a mapping of HypoEnergy-KI to the multiple- choice knapsack problem and use dynamic programming to address the problem. HypoEnergy-KN considers the optimization for the known workload but in the case of having a nonideal supercapacitor bank that leaks energy. Evaluations on iPhone load measurements demonstrate the efficiency and applicability of the HypoEnergy framework in extending the system’s lifetime.