Conjugate gradients minimizer

Gareth McCaughan Gareth.McCaughan at pobox.com
Wed Mar 26 22:24:34 CET 2003


Carl Banks wrote:

> But let me recommend something else.  You have only a thousand
> variables, which is really not a lot.  Conjugate gradient is best
> suited for systems of millions of variables, because it doesn't have
> to store a matrix.  It doesn't scale down well.
> 
> So, unless you have reason to believe conjugate-gradient is specially
> suited to this problem (indeed, I have heard of an atomic structure
> problem that was like that), or if you plan to scale up to DNA
> crystals someday, use the BFGS method instead.

I concur. If it turns out that the overhead from BFGS
*is* too much for some reason, you might also consider
something intermediate between conjugate gradient and
BFGS, such as L-BFGS.

But it's not true that BFGS requires inverting a matrix
at each step. The matrix you maintain is an approximation
to the *inverse* of the Hessian, and no inversion is
necessary.

-- 
Gareth McCaughan  Gareth.McCaughan at pobox.com
.sig under construc




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