In this paper, we consider the power optimization problem in Orthogonal Frequency Division Multiplexing (OFDM)-based relay-enhanced device-to-device (D2D) communication. In a single cell transmission scenario, dual-hop communication is assumed in which each D2D user re-uses the spectrum of just one Cellular User (CU). In this work, we formulate a joint optimization scheme under a Decode-and-Forward (DF) relaying protocol to maximize the sum throughput of D2D and cellular networks via power allocation over different sub-carriers. The problem is thus transformed into a standard convex optimization, subject to individual power constraints at different transmitting nodes. We exploit the duality theory to decompose the problem into several sub-problems and use Karush–Kuhn–Tucker (KKT) conditions to solve each sub-problem. We provide simulation results to validate the performance of our proposed scheme.