In this paper, transmit beamformer design problem is considered for single group multicast case. This problem is treated in discrete phase and amplitude and converted to a linear form. The solution of this linear optimization problem is always feasible as long as the total transmit power is above a certain value. The proposed method is guaranteed to find the optimum solution. This new approach is used to design discrete phase-only (DPOB) and discrete phase-amplitude beamformers (DPAB). It is shown that the proposed technique returns even better beamformers compared to its continuous counterparts with significantly improved computational complexity in comparison to brute force approach. When the channel state information (CSI) is partly available, robust beamformers should be used. In this paper, robust DPOB (RDPOB) and robust DPAB (RDPAB) are proposed for this purpose. It is shown that robust discrete beamformers generate better performance improvement compared to its robust continuous beamformers. Several experiments are done in order to show both the performance gain and computational complexity of the proposed techniques. (C) 2014 Elsevier Inc. All rights reserved.