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We formulate and analyze the problem of optimal downlink scheduling with instantaneous channel and queue size information when both power and bandwidth may be adaptively split among multiple users. We derive optimal solutions of low computational complexity, as well as faster and simpler approximations, to various versions of this problem when the power, rate, and bandwidth allocations to the users can all take continuous values. For this case, we show that the optimal scheme requires transmission to no more than two users during each time slot when users can receive at arbitrary rates, even when the user rate per unit of bandwidth is upper bounded by the best available modulation scheme. Our methods also extend easily to incorporate other intuitive constraints such as upper limits on user rates to improve frame fill efficiency. Simulation results suggest that the simple approximations work nearly as well as the throughput optimal schemes when continuous bandwidth and power partitions are allowed. In practice, the rate and bandwidth assignments to users take discrete values, and we present heuristic methods motivated by the continuous optimum to this discrete case.