Future mobile radio networks are expected to witness an increase in capacity demand. Since the spectrum suited for mobile radio application is scarce, the spectrum efficiency of future mobile radio networks has to be increased in order to be able to meet the capacity demand. In networks applying adaptive modulation and coding, both, transmit power and bandwidth can be considered as resources. In order to achieve high spectrum efficiency, the adaptation of the allocation of transmit power and bandwidth to the time-varying capacity demand is an important topic. In this paper, an approach that adjusts the allocation of transmit power to the cells in order to adapt the network to changing capacity demands is proposed. A mathematical model that relates transmit power and the probability of outage in the cells is presented and used in an approach for the minimsation of the outage probability in the cells using convex optimisation techniques. The performance of the presented approach is evaluated and its suitability for the adaptation of the network to capacity hotspots is shown. Due to the use of a mathematical model and convex optimisation techniques, the presented approach is suited for self-organising optimisation.