[Ipopt] quasi-newton method internals

[Ipopt User]

Thanks, if you have a block matrix X = [H A; A' I], then the Sherman-Morrison
formula can be used for rank-1 updates to H: [H+VV' A; A' I] = [H A; A' I]
+ WW' with W=[V;0].

I still wonder why IPOPT uses matrix inversion instead of cholesky or LU
factorization. I have read that the cholesky factorization is numerically
better, but can't find where anymore.

On Wed, Nov 12, 2014 at 2:41 PM, Ian Washington <washinid at mcmaster.ca>
wrote:

> I'm no expert on the implementation/logic details, but the there seems
> to be some description of the details on pgs 102 to 109 from Larry
> Biegler's book on nonlinear programming -->
> http://epubs.siam.org/doi/book/10.1137/1.9780898719383
>
> Ian.
>
> On 11/12/2014 02:10 PM, Ipopt User wrote:
> > The quasi-newton method in IPOPT is not described in any publication as
> far
> > as I can tell. I am trying to understand its specifics, especially how it
> > exploits the low rank of the Hessian to solve system (13) in
> > http://www.optimization-online.org/DB_FILE/2004/03/836.pdf
> >
> > The best starting point to gain insight is by looking at the changes in
> the
> > code when the quasi-newton method was added:
> >
> https://projects.coin-or.org/Ipopt/changeset?old=607&old_path=&new=608&new_path=
> >
> > I think the main logic is in these two files:
> >
> https://projects.coin-or.org/Ipopt/browser/branches/dev/LinAlg/IpLowRankUpdateSymMatrix.cpp?rev=608
> >
> https://projects.coin-or.org/Ipopt/browser/branches/dev/Algorithm/IpLowRankAugSystemSolver.cpp?rev=608
> >
> > In the latter file, it seems as the Sherman-Morrison formula is used
> (line
> > 152), but I don't see where. I also don't see how the inverse of W_k
> could
> > make solving (13) easier. Why is the inverse of the Hessian used (I
> > remember reading that a cholesky factorization is numerically superior
> > while SNOPT uses LU factorization)? I'm not looking for a full
> explanation,
> > but a few hints would be greatly appreciated, thanks.
> >
> >
> >
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> > Ipopt at list.coin-or.org
> > http://list.coin-or.org/mailman/listinfo/ipopt
> >
>
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