[Ipopt] IPOPT Questions on DOF and feasibility

[David Veerasingam]

Hello all,

I have a few questions about IPOPT's operation.

1) IPOPT sometimes exits when the number of constraints exceed the number of
variables (it complains that there are too few degrees of freedom). This
sometimes happens in the final steps of a shrinking horizon MPC application
(where variables at each instance are successively fixed as one marches
toward the endpoint). GRG solvers like CONOPT however continue to chug on,
even when there are limited degrees of freedom. I understand IPOPT's
behavior arises because it drops fixed variables from the problem. Is there
a setting to prevent IPOPT from dropping the fixed variables when solving an
NLP?

When IPOPT exits on a "too few degrees of freedom" error, I do kind of think
it's the correct response from a mathematical point of view (the problem is
probably incorrectly modeled in some sense). But it would be great if it
could be made to proceed gracefully nonetheless, especially in control
applications.

2) IPOPT sometimes converges to an infeasible point from a mere change in
objective function. I'm having trouble understanding why this can happen.
For instance, I solve an NLP once with a setpoint tracking objective, and it
converges to an optimal solution. Using that solution as an initial guess
(the default behavior in AMPL), I change the objective function to an
economic objective function and re-solve (everything else stays exactly the
same), and it converges to an infeasible point. If I start from a feasible
point, doesn't the filter method ensure I don't lose feasibility?

Extra info: my ipopt.opt file is as follows.

linear_solver ma27
max_iter 12000
print_level 4
tol 1e-8
acceptable_tol 1e-6
expect_infeasible_problem yes
linear_system_scaling mc19
linear_scaling_on_demand no
warm_start_init_point yes
mu_strategy adaptive

I'd be grateful if someone could shed some light on these issues. Thank you
so much.
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