In this paper we apply constrained optimization techniques to optimally allocate bandwidth and transmit power to the users in a cellular network. We utilize partial frequency reuse as inter-cell interference mitigation technique considering multiple users uniformly located in the cell. Efficient algorithms are proposed to select the user in the cell regions. Moreover, based on user's selection the maximization of the minimum rate is used to optimally allocate the bandwidth and power to the users. We further demonstrate by simulations that using partial frequency reuse as inter-cell interference mitigation technique is more efficient in power use than using frequency reuse-1 or frequency reuse-3.