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Orthogonal frequency division multiplexing (OFDM) is the key component of many emerging broadband wireless access standards. The resource allocation in OFDM uplink, however, is challenging due to heterogeneity of users' quality of service requirements, channel conditions, and individual resource constraints. We formulate the resource allocation problem as a non-strictly convex optimization problem, which typically has multiple global optimal solutions. We propose a reduced primal-dual algorithm, which is distributed, requires simple local updates, and probably globally converges to a global optimal solution under easily satisfied suficient technical conditions. The performance of the algorithm is studied through a realistic OFDM simulator based on field measurements. Compared with the previously proposed standard primal-dual algorithm, the reduced algorithm decreases the total number of iterations by 80% and the variance by 85%.