On Sat, May 19, 2007 at 07:08:55PM -0400, Kostas Oikonomou wrote:
> Unfortunately, even though the (entropy) function is
> very-well behaved, symbolic solution is impossible for any
> but the simplest problems. In this particular case, I was
> just trying the augmented Lagrangian method, and I thought I
> would start with a rather toy problem.
>
> A more typical problem for what I'm trying to do would be an
> h(x_1,..,x_20), with 5 or 10 linear constraints.
Even if your problem is not solvable completely via symbolic methods,
it may be worth it to apply symbolic methods to reduce your problem
prior to using numerical methods such as augmented_lagrangian.
For example, by eliminating certain variables using the same
techniques that stavros suggested, you can reduce dimensionality and
perhaps make the numerical method work better. It's worth a try on
your "real" problems.
Also, it can be useful to apply symbolic methods to try to check your
answer, for example by examining behavior in the viscinity of the
result you find numerically.
These are of course just general comments that tend to apply to
anything that one does in a CAS system.
--
Daniel Lakeland
dlakelan at street-artists.org
http://www.street-artists.org/~dlakelan