We apply constrained optimization techniques to optimally allocate the bandwidth and power to the users in a cellular network. We investigate partial frequency reuse with multiple users in the full and partial frequency regions for inter-cell interference mitigation. We show that the non-convex sum-rate maximization problem becomes convex under certain simplifying assumptions. Moreover, an efficient algorithm is developed to solve the problem for a fixed bandwidth allocation. The optimal

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... n assigns all available power to the users. Finally, we prove that even without simplifications the non-convex problems of maximizing the minimum rate among users and minimizing the sum-power are transformable into convex forms.