The joint power control and base station (BS) assignment problem is considered under Quality-of-Service (QoS) constraints. If a feasible solution exists, the problem can be efficiently solved using existing distributed algorithms. Infeasibility is often encountered in practice, however, which brings up the issue of optimal admission control. The joint problem is NP-hard, yet important for QoS provisioning and bandwidth-efficient operation of existing and emerging cellular and overlay/underlay networks. Recognizing this, there have been several attempts to develop reasonable heuristics for joint admission and power control. This contribution takes a more disciplined approach. The joint problem is first concisely formulated as a constrained optimization problem, whose objective combines the BS assignment, admission, and power control components. The formulation also allows for multicasting. A geometric programming approximation is then developed, which forms the core of a heuristic, yet well-motivated centralized algorithm that generates approximate solutions to the original NP-hard problem. Numerical results against an enumeration baseline illustrate the merits of the approach.