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To realize cooperative computation and communication in a relay mobile edge computing system, we develop a hybrid relay forward protocol, where we seek to balance the execution delay and network energy consumption. The problem is formulated as a nondifferentialbe optimization problem which is nonconvex with highly coupled constraints. By exploiting the problem structure, we propose a lightweight algorithm based on inexact block coordinate descent method. Our results show that the proposed algorithm exhibits much faster convergence as compared with the popular concaveconvex procedure based algorithm, while achieving good performance.