Load balancing is one of the key target of LTE Self-Optimization Network (SON). In this paper, we propose a load balancing method for LTE downlink network, namely Load Vector Minimization based Load Balancing (LVMLB) method. Load Vector (LV) is a vector whose elements are the load values of cells and sorted in descending order. The order of LVs is defined by the lexicographical order. The smaller the LV is, the higher the balance degree of cells load will be.

As the LV has a lower bound with total load fixed, the balance degree of cells load would reach a local optimal. On this basis, we design the LVMLB algorithm, trying to get the optimal solutions to load balancing problems, the proof of being optimal will also be given in this paper. Simulation scenarios are set in a square part of Macro-Pico mixed HetNets. Simulation results show that LVMLB outperforms the Cell Region Expansion (or Bias) scheme, increasing the capacities of Macro and Pico tiers at the same time, and improving balance degree of cells load, only sacrificing a little QoS performance.