A Convex Optimization Approach to Curve Fitting with B-splines

This paper presents a new framework for approximating data with smooth splines. The classical spline approximation problem is reformulated as a convex optimization problem, in which both the required number of knots and the knot locations are found automatically and simultaneously. Spline constraints are easily added to improve the quality of the approximation. Three examples are presented to illustrate the effectiveness of the proposed framework. The obtained numerical results show improvements of the smoothness of two benchmark problems and show that more complex constraints can be included.status: publishe