The electrodeless fluorescent lamp offers a long-life, efficacious alternative to conventional reflective lighting, but the ballast design is formidable due to the interaction between the lamp and ballast. The interaction exists for two reasons. First, the arc resistance is highly dependent upon the power density. Second, the output power of the resonant converter is a strong function of the load resistance. Soft switching, essential to the efficient and reliable functioning of the power converter, complicates the design process. This paper presents a robust design methodology, via nonlinear programming (NP), where the transition interval and midpoint capacitance are critical elements of the solution. Analytical expressions are offered as ingredients of the parameter optimization. Minimizing the RMS current flow through the active switches yields peak efficiency. In this case, the converter operates with zero-voltage switching (ZVS) and zero-current switching (ZCS), with nonzero values of midpoint capacitance. Excellent agreement between the analytical and physical models was achieved. The efficiency of the physical model was found to exceed 90%.