With recent developments in low-thrust spacecraft propulsion, numerous types of orbit transfers can now be achieved. It is critical that these transfers be optimized to achieve maximum efficiency in both energy use and time-of-flight. As is often the case, optimization of these mission parameters is performed in accordance with non-linear constraints imposed on the spacecraft properties and/or its orbital elements. Thus, a robust non-linear constrained optimization method must be chosen to properly address these issues. However, which type of optimization method to chose is important, since some algorithms may lead to better or faster convergence when compared to others. To address this issue, several non-linear constrained numerical optimization methods have been coded in Matlab® and implemented in Satellite Toolkit's Astrogator®, in order to determine what methods, if any, perform better for varying low-thrust orbit transfer scenarios.