Power control in wireless cellular networks is crucial in minimizing power consumption, mitigating interference, increasing network capacity, and maintaining link quality of service (QoS). Robustness to variation in noise level and accommodation of QoS constraints are particularly important practical issues. These issues in power control are transformed into two convex optimization problems that have efficient algorithms. The first convex power control formulation is robust optimization and its variation: robust Pareto optimization. The second convex formulation is QoS constrained optimization and its two extensions on proportional and min-max fairness implementations. These results also lead to new admission control and relative pricing schemes. As concurred by simulations, these convex optimization formulations optimize power and control QoS in a robust, optimal, fast, scalable and versatile way.
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