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In this paper, we investigate the energy-efficient power control for device-to-device (D2D) communications underlaying cellular networks, where uplink resource blocks allocated to one cellular user equipment are reused by multiple D2D pairs and co-channel interference caused by resource sharing becomes a significant challenge. We consider both the total energy efficiency (EE) and individual EE optimization problems, which are fractional programming and generalized fractional programming problems, respectively, and are hard to tackle due to their non-concave nature. We first transform them into equivalent optimization problems in parametric subtractive forms, which fit in a class of non-concave optimization methods known as difference of two concave functions programming, and then solve them using Dinkelbach and branch-and-bound methods to give global optimal solutions. Due to the unaffordable …