In this paper, we propose piecewise mixed integer linear programming (PWMIP) models for joint subcarrier and power allocation in downlink wireless orthogonal frequency division multiple access (OFDMA) networks. In particular, we consider the problem of maximizing the total capacity of an OFDMA system subject to user power, subcarrier and quality of service constraints. For this purpose, we model the problem as a (0-1) mixed integer nonlinear programming problem. Then, we obtain two PWMIP models by means of a convex combination approach [
] and with the approach proposed in [
]. The latter consists of reducing the cardinality of a subset of binary variables to a logarithmic number of binary variables. Finally, we propose a variable neighborhood search (VNS) procedure [
]. Our preliminary numerical results indicate that the first model is more effective and that the VNS approach allows to obtain feasible solutions in less computational cost.