We consider scheduling and resource allocation for the downlink of a OFDM-based wireless network. During each time-slot the scheduling and resource allocation problem involves selecting a subset of users for transmission, determining the assignment of available subcarriers to selected users, and for each subcarrier determining the transmission power and the coding and modulation scheme used. We address this in the context of a utility-based scheduling and resource allocation scheme presented in earlier papers. Scheduling and resource allocation is determined by solving an optimization problem, which is convex for a reasonable model of the feasible rates. By exploiting the structure of this problem, we give optimal and sub-optimal algorithms for its solution. We provide simulation results comparing different algorithms and parameter settings.