Introduction: There has been an increasing interest in constraining transmit B1 shimming with specific absorption rate (SAR) limits [1-2], especially at high magnetic field. Since most of the existing methods rely on solving a nonconvex optimization problem, they are typically faced with two difficulties: Only local optimum solutions are obtained, and they are susceptible to the chosen initial points for optimization. Here we introduce a two stage optimization method where a reliable initial point is acquired in the first stage by a convex semidefinite relaxation (SDR) approximation method. A high quality B1 shimmed map then can be obtained in the second stage optimization using the SDR initial points. The presented technique is verified with simulations for a 16-channel transmit coil array at 7T with a human head model. Proposed Method: Denote by the complex vector where each entry defines the magnitude and phase of each RF coil. Let where represents the B1 field magnitude and phase at sample due to the th RF coil. Then the B1 field magnitude at the th sample is given by . By defining a B1 target map with uniform magnitudes at each sample (i.e., pixel) equal to , we consider the following optimization problem for homogeneous B1 shimming with an average SAR constraint