[Ipopt] Quasi-Newton approximations

[herve.martin.sc@libertysurf.fr]

Hi all,

I am trying at the moment to solve a nonlinear constrained
problem using Ipopt. It is a small scale problem (between 50
and 100 variables), whose the objective and constraints are
costly to evaluate. Nevertheless, using automatic
differentiation, I have the exact first derivatives, but not
the exact second derivatives (this is not an option in a
near future). So i use Ipopt with the limited-memory
approximation of the hessian.

Sometimes, the optimization converges very slowly. In these
cases it seems a lot of updates are skipped in the LBFGS
update. So I was wondering about the status of the various
quasi-Newton approximations in Ipopt:
- what of the SR1 update ? It is currently undocumented, and
it is specified in the code that it is not working well. Is
it a possible alternative?
- in Ipopt Fortran, the LBFGS update was implemented in two
versions, one with skipping, and the other with the Powell
correction. Would it be interesting to implement in the
current Ipopt the damped version (it seems that in Knitro
the LBFGS update uses Powell corrections)? I had a look at
the code (IpLimMemQuasiNewtonUpdater.cpp), but I have some
difficulties to figure out how to get the approximation of
the hessian at the previous iteration.
- should I instead provide to Ipopt my own approximation of
the hessian, using for example a damped dense BFGS?

Thanks in advance for any help.
Regards

Hervé MARTIN







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