Synchronous homopolar machines (SHM) with excitation winding on the stator have attracted the attention of researchers for many decades due to their high reliability. They are used in a variety of applications such as aircraft and railway generators and traction motors. At the same time, the three-dimensional structure of their magnetic circuit makes the problem of their analysis and optimization challenging. This problem becomes even more complicated when considering an SHM with hybrid excitation, with ferrite magnets in the rotor slots. The article proposes a mathematical procedure for optimizing a synchronous homopolar generator with hybrid excitation based on the single-criterion Nelder-Mead method and two-dimensional finite element analysis (FEA). The use of the Nelder-Mead method compared to multicriteria methods and 2D FEA compared to 3D FEA makes possible to significantly reduce the computational burden. As a result of optimization, the power loss and torque ripples of the generator are significantly reduced. The article also compares the characteristics of synchronous homopolar generators with and without ferrite magnets.