Re: Nonlinear CG

Peter, Andrew,
One of the minimizers I've used has documentation here:
www.nag.co.uk/numeric/CL/nagdoc_cl08/pdf/E04/e04dgc.pdf
fThe documentation says "[it] minimizes an unconstrained nonlinear function
of several variables using a pre-conditioned, limited memory quasi-Newton
conjugate gradient method. The function is intended for use on large scale
problems." I'm not sure how that algorithm would compare with Newton-Krylov.


I would assume a minimizer that can take advantage of grad f would generally
be better, but I am not a minimizer expert. (That, of course, would require
a DifferentiableScalarValuedFunction concept rather than just the Matrix
concept.)



—Ben




On 1/12/07, Andrew Lumsdaine <[email protected]> wrote:
>
> One approach that we used with ITL that worked fairly well was a
> matrix-free Newton-Krylov approach (cf Brown and Hindmarsh).  I think ITL
> has example code for this in one of the subdirectories.
>
> Cheers,
> Andrew Lumsdaine
>
> On Jan 12, 2007, at 11:42 AM, Peter Gottschling wrote:
>
> Hi Ben,
>
> I'm not an expert of non-linear solvers.  Most things I have seen (a while
> ago) were approximated Newton schemes with Jacobi matrix was approximated
> from the operator.  This requires (I think) that one has a matrix
> representation of the operator which I'm afraid you probably don't.
>
> Regarding pseudocode or free software I would need to search too.
>
> Best Regards,
> Peter
>
> On 09.01.2007, at 18:38, Ben FrantzDale wrote:
>
> Peter,
> Interesting. I'll start thinking about it.
>
> I think most nonlinear CG flavors require one additional concept: a
> function,
>   func(const vector& x, scalar& result, vector& result_gradient),
> which computes f(x) and f'(x).
>
> I actually don't want to use PETSc data. My state vector represents atom
> positions as well as continuum displacements, stored separately, so
> basically it's a heterogeneous mess. (This is part of the reason a generic
> approach seems so appealing – I should be able to abstract that
> heterogeneity away.)
>
> Do you know where I might find pseudocode (or just Free code) for of
> algorithm?
>
> —Ben
>
>
> On 1/9/07, *Peter Gottschling* < [email protected]> wrote:Dear Ben,
>
>
> As far as I know, non-linear solvers does not exist in ITL.  It is an
> excellent idea and we will likely work on it in the future.  If you
> want to work on this, I'd be happy to support you.
>
> I don't know if that helps you, I've written an interface between PETSc
> and parallel BGL so that one can read out parallel PETSc matrices from
> generic libraries and also access to distributed PETSc vector without
> copying them.  However, it sounds more that you want to use PETSc data
> with in a clearer way than I did. ;-)
>
> Best Regards,
> Peter
>
> On 09.01.2007, at 18:01, Ben FrantzDale wrote:
>
> > Dear ITL-devel,
> > I'm glad I finally found ITL. It looks like it could be the Right Way
> > to solve a bunch of problems that various closed-source Fortran
> > libraries have attempted.
> >
> > I am interested in solving large nonlinear minimization problems in
> > parallel. Presently we are experimenting with several CG solvers. The
> > work, but all of them want to see the state vector as a single
> > contiguous array of doubles. The ITL example using PETSc in parallel
> > makes me think there are interesting possibilities for large nonlinear
> > problems as well.
> >
> > The ITL distribution includes two nonlinear examples, but all of the
> > solvers appear to be linear. Has anyone extended ITL to do nonlinear
> > minimization?
> >
> > Again, great work.
> >
> > Thanks,
> > Ben FrantzDale_______________________________________________
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> ------------
> Peter Gottschling, Ph.D.
> Research Associate
> Open Systems Laboratory
> Indiana University
> 135 Lindley Hall
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> ------------
> Peter Gottschling
> Research Associate
> Open Systems Laboratory
> Indiana University
> 135 Lindley Hall
> Bloomington, IN 47405
> Tel.: +1-812-855-3608   Fax: +1-812-856-0853
> http://www.osl.iu.edu/~pgottsch <http://www.osl.iu.edu/%7Epgottsch>
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