An iterative convex element position optimization algorithm is proposed for linear phased array synthesis with the aim of minimizing the side lobe level at multiple scan angles in the presence of mutual coupling. Embedded element patterns are obtained via full-wave simulations and integrated into the optimization procedure. A two-step optimization scheme with a smart initial array layout selection is proposed and analyzed. Conventional H-plane patch antenna arrays are used for algorithm demonstration. The simulation results show that via position-only optimization, the maximum side lobe level can be significantly decreased compared to the benchmark regular arrays with a half-wavelength spacing while keeping a similar total array length.@en