Recursive construction of optimal smoothing splines with constraints

This paper considers the problem of recursively constructing smoothing spline curves with equality and/or inequality constraints each time when a new set of data is observed. The splines are constituted by employing normalized uniform B-splines as the basis functions. It is shown that various types of constraints are formulated as linear function of the so-called control points, and the problems reduce to convex quadratic programming problems. Then, a recursive algorithm for constructing such constrained smoothing splines is developed. We demonstrate the effectiveness and usefulness by numerical examples.