Adaptive Curve Tailoring

This paper deals with the problem of finding an average of several curves subject to qualitative constraints and restrictions on the curves. The unknown average curve is the solution of a weighted least squares problem involving the deviation between the given curves and the unknown curve. The qualitative constraints are that some curves are preferred compared to other curves. The qualitative information is converted into constraints on the weights in the least squares problem defining the average curve. The model defining the curves is parameterized and restrictions on the curves are defined in terms of restrictions on the parameters. We give an example where the curves determined from three data sets are required to be monotone and convex. We also show that one curve being preferred restricts the set of possible curves that can be an average curve.