Re: time-series smoothing

From: A.G.McDowell (mcdowella_at_mcdowella.demon.co.uk)
Date: 03/17/05 

Date: Thu, 17 Mar 2005 19:09:58 +0000

In article <4239ACF1.55B96907@ever.com>, Jake <wh@ever.com> writes
>I have a problem of an apparent cross-disciplinary nature so I hope that
>justifies the cross-posting.
>
(trimmed)
>
>2] Would it make sense to use Nelder-Mead (downhill simplex) method for
>minimizing, even though this problem seems to be a constrained
>optimization? There are three parameters, all constrained to positive
>values and one constrained to integer values, so differentiation doesn't
>seem to be an option. Is there a better derivative-free optimizer for
>this problem? Is there a differentiation method that would work better,
>even for a function that is only partially differentiable?
>
I note that the Nelder-Mean algorithm is mentioned in Numerical Recipes
to need restarting in practice and is now known to sometimes fail to
converge (google on Nelder simplex counter-example yields e.g.
http://portal.acm.org/citation.cfm?id=589108: the body of the text
requires a subscription, but the abstract is accessible to all). Torczon
has provided a variety of convergence proofs for direct search
algorithms, one of which looks like a variant of the Nelder-Mead
algorithm: googling on Torczon Simplex yields http://www.cs.wm.edu/~va/r
esearch/, which includes a paper "On the convergence of the
multidirectional search algorithm".

Are these methods destined to replace Nelder-Mead? Nice Theoretical
curiosities? Something in between? 

-- 
A.G.McDowell

Relevant Pages

  • Re: time-series smoothing
    ... Is there a differentiation method that would work better, ... I note that the Nelder-Mean algorithm is mentioned in Numerical Recipes ... Are these methods destined to replace Nelder-Mead? ...
    (sci.math.num-analysis)
  • Re: time-series smoothing
    ... Is there a differentiation method that would work better, ... > I note that the Nelder-Mean algorithm is mentioned in Numerical Recipes ... one of which looks like a variant of the Nelder-Mead ... > multidirectional search algorithm". ...
    (sci.math.num-analysis)
  • Re: time-series smoothing
    ... Is there a differentiation method that would work better, ... > I note that the Nelder-Mean algorithm is mentioned in Numerical Recipes ... one of which looks like a variant of the Nelder-Mead ... > multidirectional search algorithm". ...
    (sci.stat.edu)
  • Re: time-series smoothing
    ... >I note that the Nelder-Mean algorithm is mentioned in Numerical Recipes ... >has provided a variety of convergence proofs for direct search ... one of which looks like a variant of the Nelder-Mead ...
    (sci.math.num-analysis)
  • Re: time-series smoothing
    ... >I note that the Nelder-Mean algorithm is mentioned in Numerical Recipes ... >has provided a variety of convergence proofs for direct search ... one of which looks like a variant of the Nelder-Mead ...
    (sci.stat.edu)