In this article, power allocation in cellular networks considering Nakagami- m fading is proposed. The objective is to optimize the network energy efficiency and throughput subject to user outage probability constraints. The moment generating function (MGF) is used to derive the exact outage probability over Nakagami- m fading channels. Further, tight upper and lower bounds on the outage probability are derived using the Weierstrass, Bernoulli and exponential inequalities. These bounds are used to characterize the relationship between outage probability and normalized signal to interference plus noise ratio (SINR) in Nakagami- m fading. Power allocation algorithms for throughput maximization and energy efficiency are proposed. The throughput maximization problem has a logarithmic form so a differential method is used to solve this problem. The proposed energy efficiency problem has a nonconvex fractional program form so a parametric transformation is used to convert it to a subtractive optimization problem which can be solved iteratively. Simulation results are presented which show that the proposed schemes provide better performance than existing methods in terms of power consumption, throughput, energy efficiency and outage probability.