Hello,

I have a numerical problem of smoothing natural cubic spline with a number of tabulated data.
It has a "smoothing" parameter which gives more importance to the errors between the fitted curve and the input numbers vs the total curvature of the fitted spline.
something like nag_smooth_spline_estim
but with choosing the smoothing parameter manually.

I wish to add to this problem a new constraint such that the convexity of the fitted spline doesn't change, that is if it is convex it should be convex throughout the tabulated points, and if it is concave it should be concave throughout.

Perhaps, there is a range of smoothing parameters which satisfy that convexity doesn't change

Is this a previously studied problem? Are there any papers/references?

best regards,