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An important performance measure in wireless networks is the manner in which the network can distributively manage its limited energy and spectrum resources, while assuring certain quality of service for communicating users. The current practice is to develop schemes with low complexity that are based on workable, but theoretically suboptimal techniques such as random access or carrier sensing. To address the need for equally simple, but optimally performing resource management schemes, we propose a set of optimum distributed algorithms for adaptive admission control and power control, which jointly (i) maximize the number of transmitters that transmit simultaneously in shared channel(s) with a guaranteed target signal-to-interference and noise ratio (SINR) at the receiver; (ii) minimize the transmit powers required to satisfy the SINR targets; (iii) use interference measurements as the only decision-making input; and (iv) provide inadmissible links with feedback on feasible SINR for (re)admission purposes. Unlike previous studies in which SINR targets were assumed as constants, we defined these targets using arbitrary linear functions of interference. From numerical simulations, it is confirmed that the proposed scheme outperforms other schemes by achieving the theoretical performance bounds.