We consider the allocation of spectral and power resources to the mobiles (i.e., user equipment (UE)) in a cell every subframe (1 ms) for the Long Term Evolution (LTE) orthogonal frequency division multiple access (OFDMA) cellular network. To enable scheduling based on packet delays, we design a novel mechanism for inferring the packet delays approximately from the buffer status reports (BSR) transmitted by the UEs; the BSR reports only contain queue length information. We then consider a constrained optimization problem with a concave objective function - schedulers such as those based on utility maximization, maximum weight scheduling, and recent results on iterative scheduling for small queue/delay follow as special cases. In particular, the construction of the non-differentiable objective function based on packet delays is novel. We model constraints on bandwidth, peak transmit power at the UE, and the transmit power spectral density (PSD) at the UE due to fractional power control. When frequency diversity doesn't exist or is not exploited at a fast time-scale, we use subgradient analysis to construct an O(N log L) (per iteration with small number of iterations) algorithm to compute the optimal resource allocation for N users and L points of non-differentiability in the objective function. For a frequency diversity scheduler with M sub-bands, the corre- sponding complexity per iteration is essentially O(N(M^2+L^2)). Unlike previous iterative policies based on delay/queue, in our approach the complexity of scheduling can be reduced when the coherence bandwidth is larger. Through detailed system simulations (based on NGMN and 3GPP evaluation methodology) which model H-ARQ, finite resource grants per sub-frame, deployment, realistic traffic, power limitations, interference, and channel fading, we demonstrate the effectiveness of our schemes for LTE.