Subject: CCL:Grid energy minimization

From: Andreas Bender <[email-masked]>
Date: Thu, 24 Apr 2003 20:37:30 +0100 (BST)

Hi Jay,

It's related to the problem of aligning two molecules on a 3D grid for
example when using Carbo or Hodgkin similarity indices (where you try to
maximize the integral over the product of two functions that depend
on relative molecular orientation) - here the problem is not in the
minimization algorithm itself but rather in the representation at
discrete grid values.

In this case, the problem was "solved" using Gaussian representations of
molecules (e.g. Good AC, Hodgkin EE and Richards WG, JCICS 1992 (32)
188-191). The difference between the approaches is illustrated by the
problems you run into when you superimpose two _identical_ molecules using
values at grid points and a downhill (steepest gradient) optimization -
the superposition looks rather awful (I can't recall the reference right
now but can look it up if you are interested), Gaussian representations
are much more well-behaved for this task (here especially because of the
integrations one performs).

The point why it could be interesting for you: Although your task seems to
be different, you still have a function that is defined at grid
points and you wand to optimize it. Maybe you can transform your
representation of discrete points and perform the minimization in some
transformed space.

Best wishes & Good luck,
Andreas

____________________________________________

Andreas Kieron Patrick Bender
http://www.andreasbender.de

E-mail1: [email-masked]
E-mail2: [email-masked]
ICQ: 166 835 816

PhD student at Cambridge University /
Unilever Centre for Molecular Informatics
___________________________________________

On Tue, 22 Apr 2003, Jay Banks wrote:

> Hi --
>
> Does anyone have experience with minimizing potential energy functions
> defined at (or interpolated between) points on a 3-dimensional grid?
> The minimizer I've been using has occasional problems, which I think are
> associated with discontinuities at the edges of grid boxes, etc.
>
> I know that the "downhill simplex" algorithm (Nelder & Mead, Computer
> J. 7: 308 (1965)) can be useful for discontinuous functions (and/or
> discontinuous derivatives), but I doubt that it is practical for my
> purposes given the high dimensionality of my problem.  So I'd be
> interested in hearing about modifications of other "standard" methods,
> as well as anything "new" that anyone has come up with.
>
>
> Sincerely,
> Jay Banks
>
> (banks "at" schrodinger "dot" com)
>
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