The impetus of this work originated from the advent of high magnetic field magnetic resonance imaging scanners with B0 fields of 4T, 7T, and 9.4T. These ultrahigh magnetic field systems generally improve the signal to noise ratios. However, B1 field non-uniformity also occurs due to the increased RF field frequencies when wavelengths in the head become shorter than its size. As interest in multiple channel transmission line coils increases, the control of the amplitude and phase of individual coil elements is required in order to develop desired B1 field. The choice of the excitation of the coil elements may be determined by convex optimization. Convex optimization is used provides results very fast, when the problem is formulated globally. In addition, convex optimization provides better signal to noise (SNR) ratio when anatomic specific regions are investigated. In this paper, simulation and experimental results are discussed at 9.4T systems based on the number of elements. The primary objective of this study is to increase the signal in a specific target region and decrease the signal and noise in the outside region termed the suppression region. The convex formulations are minimizing the maximum field point in the suppression region while keeping the center of target maximum. Based on this min-max optimization criterion, an iteration method which modifies the selection of suppression fields is also performed to produce better results. The results of the localization on FDTD human data at 9.4T are shown in Fig. 1. In these figures, the axial slices of the center of human head model provided by XFDTD are used after manipulating with MATLAB and the 16 channel head coil is excited. Figure 1 shows an improvement of the homogeneity in the suppression region when the target region is at center. In Fig. 2, received signal localizations are obtained for three different regions of interest (ROI) after using the convex optimization. Note that the selection of ROI is limited by the geometric setting of phantom in the 8-channel TEM head coil. Convex optimization with an iterative method was performed on both the human head and phantom models with operating frequency 400 MHz to design coil channel excitation parameters. By applying the iterative method to the convex optimization, more homogeneous B1 fields are obtained in the suppression region for 9.4T system.