Note—A Note on Least Squares Fitting of Functions Constrained to be Either Nonnegative, Nondecreasing or Convex

Hudson [Hudson, D. J. Least-squares fitting of a polynomial constrained to be either non-negative, non-decreasing or convex. J. R. Statist. Soc. B.31 113–118.] has described a complicated algorithm for least-squares fitting of polynomials constrained to be either nonnegative, nondecreasing, or convex. Alternate quadratic programming formulations which approximate general functions (not necessarily polynomials) by polygonal segmentation are presented here. The technique is simpler, more general and of wider applicability than that proposed of Hudson.