[Ipopt] Good solutions with errors in derivative test

[Andrew Spiteri]

Hi all,

I am using IPOPT (MATLAB interface) to solve trajectory optimisation 
problems of medium complexity (roughly 100 variables with 300 
constraints). Due to this complexity, I am using INTLAB to automatically 
calculate the gradient, Jacobians and Hessians, however I am now 
noticing that the IPOPT derivative test is showing a considerable number 
of errors (in grad_f, jac_g and hess), with relative errors ranging from 
about 0.0001 to 1. I'm not sure why INTLAB seems to be giving inaccurate 
values, but I'm suspecting the various vector manipulations (scaling, 
splitting and merging) which occur in eval_f, eval_g and eval_hess.

The confusing part is that the solutions actually appear as expected, 
despite these errors being present. Furthermore, solutions are typically 
found within 100 iterations, which seems to indicate a reasonably good 
performance. So my question is: is it possible to have good solutions 
with good performance when the aforementioned errors are present in the 
problem?

Thanks in advance.
Andrew Spiteri