Fast First-Order Algorithm for Large-Scale Max-Min Fair Multi-Group Multicast Beamforming

We propose a first-order fast algorithm for the weighted max-min fair (MMF) multi-group multicast beamforming problem suitable for large-scale systems. Utilizing the optimal multicast beamforming structure obtained recently, we convert the nonconvex MMF problem into a weight minimization problem. We show this problem is a weakly convex problem and propose using the projected subgradient algorithm (PSA) to solve it directly, avoiding the conventional method for the MMF problem that requires iteratively solving its inverse problem, which is computationally expensive. We show the convergence of PSA, although our problem is only weakly convex. A method for a suitable initial point to accelerate convergence is also presented. Simulation results show that PSA offers near-optimal performance with considerably lower computational complexity than existing methods for large-scale systems.