Heterogeneous networks (HetNets) with a topology of mixed macro-cells and low-power nodes (LPNs) form an important step of capacity enhancement for LTE and LTE-A. In this paper, we present an optimization framework for load balancing in LTE HetNets, by means of cell range assignment using cell-specific offset. For any given offset setting, the resulting cell load is effectively approached via the solution of a system of non-linear equations characterizing the load-coupling relation between cells. We present a computationally efficient bounding scheme to approximate the solution of the non-linear system and provide theoretical insights into the monotonicity and convergence of the scheme. The bounding scheme is embedded into an algorithm based on the principle of design of experiments (DOE) for cell offset optimization. Simulation results demonstrate the effectiveness of the optimization process for LTE load balancing with HetNet elements.