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In this paper, we consider an amplify-and-forward wireless relay system where multiple source nodes communicate with their corresponding destination nodes with the help of relay nodes. Conventionally, each relay equally distributes the available resources to its relayed sources. This approach is clearly sub-optimal since each user experiences dissimilar channel conditions, and thus, demands different amount of allocated resources to meet its quality-of-service (QoS) request. Therefore, this paper presents novel power allocation schemes to i) maximize the minimum signal-to-noise ratio among all users; ii) minimize the maximum transmit power over all sources; iii) maximize the network throughput. Moreover, due to limited power, it may be impossible to satisfy the QoS requirement for every user. Consequently, an admission control algorithm should first be carried out to maximize the number of users possibly served. Then, optimal power allocation is performed. Although the joint optimal admission control and power allocation problem is combinatorially hard, we develop an effective heuristic algorithm with significantly reduced complexity. Even though theoretically sub-optimal, it performs remarkably well. The proposed power allocation problems are formulated using geometric programming (GP), a well-studied class of nonlinear and nonconvex optimization. Since a GP problem is readily transformed into an equivalent convex optimization problem, optimal solution can be obtained efficiently. Numerical results demonstrate the effectiveness of our proposed approach.