In this paper, we consider the problem of joint antenna selection and analog beamformer design in downlink single-group multicast networks. Our objective is to reduce the hardware costs by minimizing the number of required phase shifters at the transmitter while fulfilling given distortion limits at the receivers. We formulate the problem as an L0 minimization problem and devise a novel branch-and-cut based algorithm to solve the resulting mixed-integer nonlinear program to optimality. We also propose a suboptimal heuristic algorithm to solve the above problem approximately with a low computational complexity. Computational results illustrate that the solutions produced by the proposed heuristic algorithm are optimal in most cases. The results also indicate that the performance of the optimal methods can be significantly improved by initializing with the result of the suboptimal method.