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We present an algorithm to dynamically allocate transmission power to maximize the throughput-utility in an interference-limited network under an instantaneous sum power constraint with time-varying channels. We consider the equivalent problem of maximum admission with queue stability constraint through Lyapunov optimization. The resultant non-convex minimization problem is solved by an online algorithm consisting of two components: first, successive convex approximations to randomly choose a local minimum, and second, a modified pick-and-compare method for low-complexity convergence to a global minimum. We prove the optimality of this approach, derive its tradeoff between throughput-utility and delay, and demonstrate its performance advantage against existing methods.