[Ipopt] Robustness of IPOPT

[Marco Hülsmann]

Dear IPOPT mailing list members,

I communicated with Prof. Andreas Wächter this week, who told be that he is no longer involved in IPOPT and
suggested me to contact the IPOPT mailing list.

I have the following request:

We at Fraunhofer SCAI (Sankt Augustin, NRW, Germany) use IPOPT in the research project BePhaSys. For more information, cf. 

http://www.scai.fraunhofer.de/en/business-research-areas/simulation-engineering/projects/bephasys.html

We have spent a considerable amount of time on programming the interface to our NLP.
Unfortunately, we cannot achieve convergence to a global optimum in all of our applications using IPOPT. Curiously, a simple Newton-Lagrange optimizer with Armijo step length control (using an exact L1 penalty function) converges to the optimum in all applications (using the same interface).

We have tried different parameter settings for IPOPT (various perturbations of the hessian, bound_push, multiplier updates and some more) but have not found a parameter combination that matches all of our test cases. Do we overlook something essential?

A short characterization of the application: We aim to minimize the Gibbs energy of chemical systems with multiple components in order to identify the active phases. First, a global estimation technique produces a set of feasible starting points. Second, a local optimization (IPOPT or Newton-Lagrange-Armijo) is started from all of these points. The arising NLPs have the following characteristics:
- search space dimension: 10-100
- relatively cheap evaluations of the objective function and its derivatives
- linear as well as quadratic equality constraints
- linear inequality constraints
- optima may be very close to the boundary
- objective function grows to infinity at the boundary (no continuous continuation of the objective function)
- some application problems are convex, some are not

When starting IPOPT with hessian perturbation, most of our test cases fail.
With hessian perturbation switched off (max_hessian_perturbation = 0), only the convex test cases work.

In general, have you any ideas to achieve more robust behavior with IPOPT?
We are very much looking forward to getting an answer.

Kind regards,
Dr. Marco Hülsmann

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Dr. rer. nat. Marco Hülsmann (Dipl.-Math.)
Fraunhofer-Institut für Algorithmen und Wissenschaftliches Rechnen (SCAI)
Abteilung Simulationsanwendungen
Schloss Birlinghoven, 53757 Sankt Augustin

Tel. +49 2241/14-2053
Fax  +49 2241/14-1368