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Orthogonal frequency division multiplexing (OFDM) with dynamic scheduling and resource allocation is a key component of most emerging broadband wireless access networks such as WiMAX and LTE (long term evolution) for 3GPP. However, scheduling and resource allocation in an OFDM system is complicated, especially in the uplink due to two reasons: (i) the discrete nature of subchannel assignments, and (ii) the heterogeneity of the users' subchannel conditions, individual resource constraints and application requirements. We approach this problem using a gradient-based scheduling framework. Physical layer resources (bandwidth and power) are allocated to maximize the projection onto the gradient of a total system utility function which models application-layer Quality of Service (QoS). This is formulated as a convex optimization problem and solved using a dual decomposition approach. This optimal solution has prohibitively high computational complexity but reveals guiding principles that we use to generate lower complexity sub-optimal algorithms. We analyze the complexity and compare the performance of these algorithms via extensive simulations.