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This paper presents an approach to continuous variable design optimization of a power electronics converter. The objective of the optimization approach is to minimize the total component cost. The methodology is illustrated with the design of a boost power factor correction front-end converter with an input electromagnetic interference filter. The system design variables are first identified. The relevant system responses and component costs are then expressed as a function of these design variables. Finally, by using mathematical optimization techniques, the design variable values that minimize the total system component cost are obtained, given practical constraints on these design variables and system responses.