Abstract: We adopted the uniform B-spline in building the robust models for interpolation problems of interval data. Compared with the robust models of the traditional polynomial spline, the B-spline models proposed in this paper have a number of advantages that enable a solution of an obvious finite convex optimization problem due to more concise formulations and a more simplified computing process. We put forward the method of creating the characteristic polygon vertices based on the given interval data for the purpose of increasing the freedom degree of models. The robust optimization models of the frequently used uniform quadratic and cubic B-spline are formulated in detail as finite convex optimization problems, which are applicable to the existing optimization algorithms and software. Some numerical examples are presented to show the feasibility and effectiveness of the proposed robust models.

Key words:  interval data, interpolation, B-spline, robust model, finite convex optimization