[Coin-ipopt] number and location of non-zeros

[Andreas Waechter]

Hi Susana,

> My Jacobian and Hessian matrices are very complicated. Since it is very 
> difficult for me to find out how many non-zeros there are and where they 
> are exactly, I tried to run the program by telling it I have only 
> non-zero entries.
> For a simple example (hs071) Ipopt finds the optimal solution even 
> though the derivative checker yields plenty of errors for the Hessian 
> values. (see attached texts)
>
> I am wondering how important the information on the location of 
> non-zeros in the Jacobian and Hessian is for finding the optimum and 
> whether the above described method may be used in general (even though 
> the derivative checker shows several failures).

The correct location and values of non-zero values in the constraint 
Jacobian is absolutely crutial, since otherwise convergence will not 
happen due to incorrect linearization of the constraints.

If the information about the Hessian matrix is incorrect, Ipopt can often 
still find a solution, but convergence will be slow, since it does not 
compute the correct Newton steps.

I hope this helps,

Andreas