Talk:Nelder-Mead method

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[edit] Formal algorithm summary needs double-checking

The description under "One possible variation of the NM algorithm" needs some rework I think. It should be checked against the algorithm description in Nelder and Mead's original paper or if that's not to hand against McKinnon's paper. I'm not convinced the current description is correct.

The notation f(\textbf{x}_{i}) is clumsy. It would be clearer to introduce something like fi.

Step 5, "shrink step", has an incoherent description

The section should then be retitled to reflect the aim as a definitive formal statement.

The structure of the algorithm is not as clearly spelled out as it could be. —Preceding unsigned comment added by 212.13.197.229 (talk) 11:42, 30 December 2007 (UTC)

I am implementing (2008.01.25) this summary in LabVIEW. So far I've noticed :

1. There is no definition on what if f(xr) == f(x1)

2. What does it mean to "compute new simplex with x" ? Does it mean replacing worst vertex with x ? Or computing new simplex using x as a "starting" vertex ?

—Preceding unsigned comment added by Kupsztal (talk) 10:05, 25 January 2008 (GMT)

The "One possible variation" section is obviously incorrect. With the suggested alpha value of 1.0, step 2 (reflection) would always yield points at the center of mass. This section should be marked incorrect/suspect to avoid confusion by readers. —Preceding unsigned comment added by Joshaller (talk • contribs) 23:51, 21 February 2008 (UTC)

[edit] reflected through the remaining N points considered as a plane

"The simplest step is to replace the worst point with a point reflected through the remaining N points considered as a plane."

I think this might be misleading or wrong. All implementations of this I've seen so far do reflect the worst point at the center of the remaining N points and not at the (hyper-)plane. Reflecting at the center is like New=Center-(Worst-Center), while reflecting at the plane would be like moving it along the plane's normal. But since I'm no expert in this field, I don't want to correct this myself. --88.73.211.225 23:33, 8 March 2007 (UTC)

Thanks. I'm no expert either, but the web pages and articles I consulted agree. So I made the correction. -- Jitse Niesen (talk) 11:49, 10 March 2007 (UTC)