Subject: CCL: Simplex optimizations in curvilinear internals

From: Dr Seth OLSEN <s.olsen1 |a| uq.edu.au>
Date: Thu, 09 Jun 2005 12:33:59 +1000

Hi CCL,

I was thinking about what a pain it can be to do numerical
gradient-driven optimizations and my thoughts turned to so-called
'simplex' methods.  It would seem that a simplex method would be quite
easy to do in cartesians, but I don't know what it would gain you. 
Mostly this is because one really wants to do optimizations in internal
coordinates, in which the energy function can take a more natural form.  

At the same time it would seem that if you create a simplex in 3N
cartesians (a total of 3N+1 points) and can project bulk rotations and
translations out of the simplex, than you would have some redundant
information that can be used to extract some (limited) gradient
information.  So for the same size simplex as the cartesian case, one
might be able to do a pseudo-gradient-guided simplex optimization in
internal coordinates that could work better.  One might be able, even,
to use the fact that curvilinear internals are usually only orthogonal
in the differential sense, not globally.

Does anyone know on the list of references, sources relating to simplex
optimization methods in curvilinear (perhaps redundant) coordinate sets?
 I've heard that simplex methods are sometimes used in molecular
dynamics simulation, but I don't know if its done in cartesians usually
or what.  Has anyone used them for quantum chemistry?

Cheers,

Seth

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Dr Seth Olsen, PhD
Postdoctoral Fellow, Computational Systems Biology Group
Centre for Computational Molecular Science
Chemistry Building,
The University of Queensland
Qld 4072, Brisbane, Australia

tel (617) 33653732
fax (617) 33654623
email: s.olsen1 |a| uq.edu.au
Web: www.ccms.uq.edu.au 

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