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We consider the joint path, subcarrier and power allocation problem for a multi-user orthogonal frequency division multiple access (OFDMA) relay-enhanced cellular (REC) network. The goal is to maximize a system utility function subject to a total transmit power constraint and the OFDMA resolver allocation constraint. Since the problem is of combinatorial complexity, we propose an iterative re-weighted minimization (IRM) framework based on reformulating the combinatorial OFDMA constraint as an equivalent continuous optimization problem. The result is a fast, globally convergent algorithm for solving the resource allocation problem in the single cell OFDMA REC network. We demonstrate the efficacy of the proposed approach and compare its performance with existing schemes through Monte Carlo simulations.