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 then propose a reduced primal-dual algorithm, which is distributed, low in computational complexity, and probably globally convergent to a global optimal solution. The performance of the algorithm is studied through a realistic OFDM simulator. Compared with the previously proposed centralized optimal algorithm, our algorithm not only significantly reduces the message overhead but also requires less iterations to converge.