[Ipopt] Meaning of dual infeasibility

[David Veerasingam]

What does it mean when my problem returns a very decent primal infeasibility
(inf_pr) but very poor dual infeasibility (inf_du)? What can I deduce from
that?

These are the last few lines of the output
--------------------------------------------------------------------------------------------------
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr
 ls
  50  5.4908440e+05 5.24e-13 9.91e+04 -11.0 1.08e-10  15.0 1.00e+00
1.00e+00h  1
  51  5.4908440e+05 1.73e-11 9.91e+04 -11.0 1.07e-10  15.4 1.00e+00
3.12e-02h  6
  52  5.4908440e+05 1.78e-11 9.91e+04 -11.0 1.51e-11  15.8 1.00e+00
3.91e-03h  9
  53  5.4908440e+05 1.79e-11 9.91e+04 -11.0 5.68e-12  16.2 1.00e+00
3.91e-03h  9

Number of Iterations....: 53

EXIT: Solved To Acceptable Level.
--------------------------------------------------------------------------------------------------

Observations:
1) My problem seems to be ill-posed at the solution point, given that lg(rg)
= 16.2. The reduced Hessian seems to be needing huge regularization
perturbations.
2) Infeasibility metrics: inf_pr = 1.79e-11, inf_du = 9.91e+04
3) This happens very frequently when I use MA57 as the linear solver; less
often with MA 27.

My ipopt.opt settings are as follows:
--------------------------------------------------------------------------------------------------
linear_solver ma57
linear_system_scaling mc19
linear_scaling_on_demand no
mu_strategy adaptive
tol 1e-8
--------------------------------------------------------------------------------------------------

Thanks!
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