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Driven by the remarkable proliferation of intelligent wireless devices, the millimeter wave (mmWave) band and beamforming technologies have been identified to be key technologies to address the pressing needs of more wireless spectrum for next-generation wireless systems. Due to the much higher frequency of the mmWave band, the path loss of the signal is significantly higher compared with traditional RF bands used by today's mobile networks. To overcome this problem, the beamforming technique has been used to compensate this loss to provide strong signal toward mobile terminals such as smartphones. However, the existing beamforming approaches are prohibitively expensive and cannot be scaled to beamforming for large scale mmWave networks. This project explores a framework for beamforming optimization in large scale mmWave networks, with multiple base stations each subject to a power budget, diverse user traffic demands, and a vast, multi-dimensional solution space for beam formation, user association, frequency reuse, and beam scheduling. We have developed innovative optimization formulations, heuristic algorithms and schemes to form a comprehensive framework for mmWave network design, including user clustering, beam resource allocation, power control, beam scheduling, and beamforming.