Tailored for the emerging class of cognitive radio networks comprising primary and secondary wireless users, the present paper deals with channel-adaptive allocation of subcarriers, rate and power resources for orthogonal frequency-division multiple access (OFDMA). Users rely on adaptive modulation and coding that they select in accordance with the limited-rate feedback they receive from the access point. The access point uses channel state information to maximize the weighted average sum-rate of the network while respecting rate and power constraints on the primary and secondary users. When the channel distribution is available, the optimal off-line allocation is obtained to benchmark performance. In addition, a simple yet optimal on-line algorithm is derived using a stochastic primal-dual approach to solve the constrained utility maximization problem formulated. Analysis and simulations corroborate that the low-complexity online recursive scheme converges to the optimal solution regardless of initialization.