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Tailored for the emerging class of cognitive radio networks comprising primary and secondary wireless users, the present paper deals with dynamic allocation of subcarriers, rate and power resources based on channel state information (CSI) for orthogonal frequency-division multiple access (OFDMA). Users rely on adaptive modulation, coding and power modes that they select in accordance with the limited-rate feedback they receive from the access point. The access point uses CSI to maximize a generic concave utility of the average rates in the network while adhering to rate and power constraints imposed on the primary and secondary users to respect cognitive radio related hierarchies. When the channel distribution is available, optimum dual prices are found to optimally allocate resources across users dynamically per channel realization. In addition, a simple yet optimal online algorithm that does not require knowledge of the channel distribution and iteratively computes the dual prices per channel realization is developed using a stochastic dual approach. Analysis of the computational and feedback overhead along with simulations assessing the performance of the novel algorithms are also provided.