Re: fmin_powell returns incorrect parameters for simple least-squares problem

On Thu, Mar 2, 2023 at 3:02 PM Matthew Brett <[email protected]>
wrote:

> Hi,
>
> On Wed, Mar 1, 2023 at 4:22 PM Robert Kern <[email protected]> wrote:
> >
> > On Wed, Mar 1, 2023 at 10:30 AM Matthew Brett <[email protected]>
> wrote:
> >>
> >>
> >> I think I'm right that we've had our own custom implementation of
> >> Powell for a very long time - it looks to me (from git blame) that
> >> Travis O put a version of the current code in with commit b94c30dcb
> >> (April 2002).
> >
> >
> > For what it's worth, it's not so much "our own custom implementation" so
> much as following a particular published variant that was explained (but
> not originally published in) Numerical Recipes. Interestingly, that chapter
> claims that the modification is to assist Powell's method in handling long
> skinny valleys.
>
> Sorry - by "custom" I only meant that we didn't import the code
> directly from somewhere else.
>
> I guess, from checking http://numerical.recipes/book/book.html - that
> this is Acton's (1970, 1990) modification of the method, referenced
> as:
>
> Acton, F.S. 1970, Numerical Methods That Work; 1990, corrected edition
> (Washington, DC:
> Mathematical Association of America), pp. 464–467.[2]
>

One of my favorites back in the day. Worth a read, if only for his
entertaining comments on the practice of numerical methods and their
occasional misapplication.


> ?   Is it really true that the modification assists Powell in handling
> long skinny valleys?   If so, does it work less well in other
> situations? Has anyone compared the algorithms across a good range of
> problems?  Should we also provide an unmodified Powell?
>
>
Chuck

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