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From: "John D'Errico" <woodchips@rochester.rr.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Is it possible to optimize a spline function?
Date: Fri, 3 Oct 2008 22:48:02 +0000 (UTC)
Organization: John D'Errico (1-3LEW5R)
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"Hailey Yang" <haileyyang@hotmail.com> wrote in message <gc64fd$i3k$1@fred.mathworks.com>...
> Thank you for your reply. My understanding for the spline approximation, which might be wrong, is that the whole region, if necessary, is seperated into different regions and each region is represented by a polynomial function.

Yes. A spline is a piecewise polynomial model,
that approximates your function from your
data points. The knots or break points specify
the locations where the pieces are tied together.


> In that case, will there be any problem with optimizing each region and then comparing the optimums to get the global optimum?

Why should there be a problem?


> I guess there is a question sort of embeded in this question, which is whether the polynomial function is always convex at the positive variable region (since variables are positive in my problem). 

There is no such constraint on a spline such
that it satisfies any convexity constraints, at
least unless you have constructed the spline
such that this is true.

 
> Another seperate question is that: is it possible to do so for multivariate spline approximation? 

Yes.

John