We consider a challenging resource allocation problem arising in mobile wireless communications. The goal is to allocate the available channels and power in a so-called OFDMA system, in order to maximise the transmission rate, subject to quality of service (QoS) constraints. Standard MINLP software struggled to solve even small instances of this problem. Using outer approximation, perspective cuts and several implementation "tricks", we are able to solve realistic instances in about one minute. A novel ingredient of our algorithm is what we call pre-emptive cut generation: the generation of cutting planes that are not violated in the current iteration, but are likely to be violated in subsequent iterations.

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OFDMA is a popular coding scheme for mobile wireless communications. In OFDMA, one must allocate the available resources (bandwidth and power) dynamically, as user requests arrive and depart in a stochastic manner. Several exact and heuristic methods exist to do this, but they all perform poorly in the "over-loaded" case, in which the user demand is close to or exceeds the system capacity. To address this case, we present a dynamic local search heuristic. A particular feature of our heuristic is that it takes fairness into consideration. Simulations on realistic data show that our heuristic is fast enough to be used in real-time, and consistently delivers allocations of good quality.

Perspective functions have long been used to convert fractional programs into convex programs. More recently, they have been used to form tight relaxations of mixedinteger nonlinear programs with so-called indicator variables. Motivated by a practical application (maximising energy efficiency in an OFDMA system), we consider problems that have a fractional objective and indicator variables simultaneously. To obtain a tight relaxation of such problems, one must consider what we call a "bi-perspective" (Bi-P) function. An analysis of Bi-P functions leads to the derivation of a new kind of cutting planes, which we call "Bi-P-cuts". Computational results indicate that Bi-Pcuts typically close a substantial proportion of the integrality gap.