[Ipopt] Hessian Computation

Chuck Teeter chuck.teeter at gmail.com
Sun Apr 4 19:36:48 EDT 2010

Hi All,

I have a question about the options available for Hessian computation in
Ipopt.  First, some background:  I use Ipopt with the AIMMS modeling system
for refinery planning.  My model makes use of some external, nonlinear
constraint functions which are implemented in C++.  For these functions, I
also use automatic differentiation to provide first partial derivatives to
AIMMS (and hence on to Ipopt).  It just so happens that in AIMMS, if
external functions are used as model constraints, second derivatives are not
made available to Ipopt for ANY constraints, either constraints implemented
natively in AIMMS, or constraints that are implemented in external

When solving my model, I set the method for Hessian computation to "exact".
It solves quickly and reliably 99% of the time without ANY Hessian
information from AIMMS.  For comparison purposes, I have also used the
quasi-newton Hessian approximation option.  It also solves reliably as well,
although it takes much longer per iteration because it now has to do much
more work.  I found these results to be somewhat curious, in that solution
reliability does not appear to be adversely affected by lack of Hessian
information or lack of Hessian quality.  I have a variety of nonlinear
constraints in my model.  Although some nonlinear constraints involve
bilinear terms, most are far more complex and are definitely 2nd order

I guess my questions boil down to these:  Is this result expected?  Would
you expect significantly improved performance/reliability if exact Hessian
information was made available to Ipopt?  Under what conditions would you
expect accurate Hessian information to be critical in achieving quick and/or
reliable solutions?

Thanks in advance for any insights!

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