[Ipopt] quasi-newton method internals

[Ian Washington]

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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