maximizing sum of squares

[Craig Markwardt <craigmnet(at)astrog.physics.wisc.edu>]

Greetings--

There are lots of packages and advice on the network concerning the
*minimization* of the sum of squares, since that is what is usually
needed for nonlinear least squares curve fitting.

I have a problem where I need to *maximize* the sum of squares.  The
application is to timing properties of astrophysical objects where one
desires to find the best-fitting signal frequency which maximizes the
amplitude.  The statistic to be maximized is distributed like a
chi-squared, but is strictly bounded at the upper end (ie, it doesn't
diverge).

For least squares problems, I typically use MINPACK-1, which works
great.  Obviously I would need to modify MINPACK to maximize instead
of minimize.  One naive way to do that would be to change the sign of
the step taken at each iteration.  Somehow I think it's more
complicated than that, however.  For example, MINPACK goes through
lots of gyrations to find an appropriate Levenberg-Marquardt
parameter, and its not evident to me that those calculations apply for
my application.

Can anybody suggest a clear way to modify the LM fitting technique for
maximization instead of minimization?

Thanks,  Craig

-- 
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Craig B. Markwardt, Ph.D.         EMAIL: craigmnet@astrog.physics.wisc.edu
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