[Ipopt] Ticket 216 - interface to MKL PARDISO

[Tony Kelman]

Alexander,

I would’ve responded to this on the ticket page you opened 
(https://projects.coin-or.org/Ipopt/ticket/216), but it appears there was an 
update to Trac today and I can’t seem to log in.

You’ve probably done the searching as well regarding past discussions on 
this topic, but I’ll include links here anyway to a few that I was able to 
find for reference's sake:

https://projects.coin-or.org/Ipopt/ticket/88
http://list.coin-or.org/pipermail/ipopt/2009-June/001583.html
http://list.coin-or.org/pipermail/ipopt/2008-January/000990.html
http://list.coin-or.org/pipermail/ipopt/2011-September/002567.html

In the 2008-2009 time frame of the first three links, the biggest issue was 
that MKL's PARDISO implementation did not calculate and/or output the 
inertia of the factorized matrix. The fourth link from 2011 indicates the 
inertia was added in a relatively recent version of MKL. Olaf Schenk 
provided a reference there to a paper "Matching-based Preprocessing 
Algorithms to the Solution of Saddle-Point Problems in Large-Scale Nonconvex 
Interior-Point Optimization" that describes the remaining feature present in 
the primary implementation of PARDISO that is not yet available (or was not 
at the time) in the MKL version. Can you comment on whether the pivoting 
algorithm described in that paper is or could be implemented in Intel MKL's 
version of PARDISO?

Glad you posted, this could be a quite helpful alternative to provide users 
of Ipopt.

-Tony