Uniqueness of Solution of Cylindricity Objective Function

Abstract

Based on the radial deviation measurement, the unconstrained optimization model is established for assessing cylindricity errors by the minimum zone method. The properties of the objective function concerned are thoroughly researched. On the basis of the modern theory on convex functions, it is strictly proved that the established cylindricity objective function is a continuous, non-differentiable and convex function defined on the four-dimensional Euclidean space R4. Therefore, the global minimal value of the objective function is unique and any of its minimal point must be its global minimal point. Thus, any existing optimization algorithm, as long as it is convergent, can be applied to solve the objective function to get the reliable minimum zone cylindricity errors. An example is given to verify the theoretical results presented.