First-order Fast Algorithms for Structurally Optimal Large-scale Multi-Group Multicast Beamforming

This thesis considers multi-group multicast beamforming design in large-scale systems, where two typical problems, the quality-of-service (QoS) problem and the max-min fair (MMF) problem, are studied. Based on the optimal multicast beamforming structure obtained recently, we propose two fast first-order algorithms to obtain the beamforming solutionsfor the QoS problem. The two algorithms both utilize the successive convex approximation (SCA) method, and they solve each SCA subproblem by the extragradient method and the alternating direction method of multipliers (ADMM), respectively. Initialization methods for SCA are also developed, including an extragradient-based approach, an ADMM-based approach, and semi-definite relaxation. Next, we propose solving the MMF problem via a simple closed-form scaling scheme, whose feasibility and bounded performance are guaranteed from the theoretical analysis. Our extensive experimental results show clear evidence of the effectiveness of our proposed methods.M.A.S