[Ipopt] how to get around an over-determined equality constrained NLP formulation

[Ian Washington]

Hello IPOPT community,

I am trying to pose an NLP where the number of equality constraints is 
greater than the number of decision variables (i.e., an over-determined 
system) and the solver immediately exits with a 
Not_Enough_degrees_Of_Freedom error.  Basically there are some equality 
constraints that fix some of the variables.

Clearly my problem is formulation related and I could reformulate the 
equality constraints to two inequality constraints using a small 
tolerance, but I rather not if possible.

Note, I'm using the matlab interface to ipopt and directly specifying 
all constraints/sparsity pattern, but I'm using the limited-memory 
Hessian approximation.

My first question: does the matlab interface expose all possible ipopt 
solver options to the user ? (I assume so, since I didn't receive any 
errors)

Second, I tried to change the fixed_variable_treatment to relax_bounds 
but it didn't seem to help. I thought this would at least prevent the 
Not_Enough_degrees_Of_Freedom error flag from occurring.

Note, I've tried this problematic formulation using knitro and the 
solver proceeds with only a warning stating that there are more equality 
constraints than variables. Also, snopt handles the problem with no issues.

Does anyone have any ideas to get around this problem.

Thanks,
Ian.

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