This paper introduces an iterative optimization framework to tackle the multi-group multicast Max-Min transmit beamforming problem. In each iteration, the optimization problem is decomposed into four sub-problems, all of which can be solved using computationally efficient algorithms. The advantage of proposed method lies in its ability to handle different types of signal constraints like total power and unimodularity; a feature not exhibited by other techniques. The proposed technique outperforms the well-known semidefinite relaxation method in terms of quality of solutions.