A novel sidelobe suppression technique is proposed for phased arrays, where only the phases of the array elements are adjusted to suppress the gain in the direction of interest while keeping the mainlobe power at a certain level. Mainlobe power constrained sidelobe suppression is formulated as a convex RSDP (Relaxed Semidefinite Program). Solution to resultant RSDP is obtained by ADMM (Alternating Direction Method of Multipliers) technique, which can handle designs for arrays with number of elements is significantly larger than that can be handled by other convex solvers such as CVX. In addition, although the available convex solvers can not provide a rank-1 solution matrix, a rank-1 solution matrix is obtained by modifying the ADMM iterations. In the conducted experiments, it is observed that proposed ADMM based method can achieve more than 10dB improvement in sidelobe levels compared to alternative techniques.