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A procedure for obtaining the optimum disk serration and blade root geometry is presented. The procedure uses the -finite element method, a suitable objective function and a standard mathematical programming technique as its basis. The objective functions investigated are the mean von Mises stress concentration factor, the coefficient of efficiency, and the hoop stress and radial stress concentration factors. The mathematical programming techniques considered are the Steepest Descent Technique, the Hill Algorithm and the Box Method. Results presented in this paper include the relative cost and the degree of success achieved by the design optimization procedure.