This thesis focusses on the development and testing of optimization methods for parameter identification in cardiac electrophysiology models. Cardiac electrophysiology models are systems of differential equations representing the evolution of the trans-membrane potential of cardiac cells. The Mitchell-Schaeffer model is chosen for this thesis. The parameters included in the Mitchell-Schaeffer model are optimally adjusted so that the solution of the model has desired properties. Two optimization problems are formulated using least-square functions to identify parameters that match phase durations and parameters that fit entire potential recordings of swine heart tissue acquired via optical imaging techniques at different stimulation frequencies. The non-differentiable optimization methods (Compass Search and three other variants) are applied to solving both optimization problems for two reasons; First, the methods are studied to evaluate performance and second, the optimization process is evaluated to confirm its ability to identify parameters for the Mitchell-Schaeffer model.