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Network-wide optimization of transmit power with the goal of maximizing the total throughput, promises significant system capacity gains in interference-limited data networks. Finding distributed solutions to this global optimization problem however, remains a challenging task. In this work, we first focus on the maximization of the weighted sum-rate capacity, as this allows the incorporation of QoS criteria in the objective function. For the case of two links, we are able to analytically characterize the optimal solution to the weighted sum-rate maximization problem. However, computing the optimal solution requires centralized knowledge of network information. We thus formulate a framework for distributed power optimization valid for N mutually interfering links, based on the concept of channel state partitioning. By assuming instantaneous knowledge of local information and statistical knowledge of non-local information, we derive a distributed power allocation algorithm, which we first analyze for the case of N = 2. Although a gain is observed over equal power allocation, the distributed algorithm shows a performance gap as compared to a centralized solution, as expected. We show however, that minimal information message passing (in this case one bit) between interfering links can help reduce this gap substantially. Finally, we also propose a method to incorporate user scheduling into the distributed power allocation algorithm.