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Previous research efforts on OFDMA resource allocation have typically assumed the availability of perfect channel state information (CSI). Unfortunately, this is unrealistic, primarily due to channel estimation errors, and more importantly, channel feedback delay. In this paper, we develop optimal resource allocation algorithms for OFDMA systems assuming the availability of only partial (imperfect) CSI. We consider ergodic weighted sum discrete rate maximization subject to total power constraints. We approach this problem using a dual optimization framework, allowing us to solve this problem with O(MK) complexity per symbol for an OFDMA system with K used subcarriers and M active users, while achieving relative optimality gaps of less than 10-3 (99.999% optimal).