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We study joint rate control and resource allocation with a packet collision constraint that maximizes the total utility of secondary users in cognitive radio networks. We formulate and decouple the original optimization problem into separable subproblems and then develop an algorithm that converges to optimal rate control and resource allocation. The proposed algorithm can operate on different time-scales to reduce the amortized time complexity. key words: utility maximization, rate control and resource allocation, cognitive radio networksdoi:10.1587/transcom.e95.b.321 fatcat:njvwbliifzh2tp4r77naytr4ai