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In this paper, we study an unmanned aerial vehicle (UAV)-assisted mobile edge computing (MEC) architecture, in which a UAV roaming around the area may serve as a computing server to help user equipment (UEs) compute their tasks or act as a relay for further offloading their computation tasks to the access point (AP). We aim to minimize the weighted sum energy consumption of the UAV and UEs subject to the task constraints, the information-causality constraints, the bandwidth allocation constraints and the UAV's trajectory constraints. The required optimization is nonconvex, and an alternating optimization algorithm is proposed to jointly optimize the computation resource scheduling, bandwidth allocation, and the UAV's trajectory in an iterative fashion. The numerical results demonstrate that significant performance gain is obtained over conventional methods. Also, the advantages of the proposed algorithm …