An original method which is based on the harmonic balance method and the OptQuest NonLinear Programs MultiStart algorithm is proposed to study the maximum vibration amplitude of periodic motion in bladed disks with dry friction dampers. In the proposed approach, the nonlinear algebraic equations obtained from the application of harmonic balance method are considered as general nonlinear equality constraints and the objective for this analysis is the maximization of the vibration amplitude. Then, the MultiStart algorithm is used to locate the global optimal solution. Finally, numerical examples show that this optimal strategy presented is reliable and effective.