  In this paper, we propose an iterative algorithm to address the nonconvex
multi-group multicast beamforming problem with quality-of-service constraints
and per-antenna power constraints. We formulate a convex relaxation of the
problem as a semidefinite program in a real Hilbert space, which allows us to
approximate a point in the feasible set by iteratively applying a bounded
perturbation resilient fixed-point mapping. Inspired by the superiorization
methodology, we use this mapping as a basic algorithm, and we add in each
iteration a small perturbation with the intent to reduce the objective value
and the distance to nonconvex rank-constraint sets. We prove that the sequence
of perturbations is bounded, so the algorithm is guaranteed to converge to a
feasible point of the relaxed semidefinite program. Simulations show that the
proposed approach outperforms existing algorithms in terms of both computation
time and approximation gap in many cases.
