[Ipopt] Optimizing without Hessian

[Philipp Bender]

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Dear list,

I play around with IpOpt trying to solve my problem and some things
from the documentation are unclear to me. Apart from that, I like the
interface a lot and compared to SLSQP from nlopt, I hope to profit
from the sparsity feature.

My question is:

What exactly does the derivative checker do?

I have the following problem:

min sum(x[i]**2), i = 0..49

s.t. -inf < x[i] < -1000

I did

* not implement eval_h and left nnz_h_lag untouched in getnlp_info()

* SetStringValue("hessian_approximation", "limited-memory");
* SetStringValue("derivative_test", "first-order");

* implement the eval_graf_f like grad_f[i] = 2*x[i]
* initialized with x[i] = i, which obviously violates bounds.

I get the following:

- ---------------------------

This is Ipopt version 3.11.9, running with linear solver mumps.
NOTE: Other linear solvers might be more efficient (see Ipopt
documentation).

Starting derivative checker for first derivatives.

* grad_f[          5] = -1.3516155659571183e+01    ~
- -1.3505262089473826e+01  [ 8.066e-04]
* grad_f[         22] =  1.0686361135565363e+01    ~
1.0667231032792877e+01  [ 1.793e-03]
* grad_f[         33] =  2.1337930046135796e+01    ~
2.1351790099452490e+01  [ 6.491e-04]

Derivative checker detected 3 error(s).

- ---------------------------

What does this mean? Is it important to have the checker run without
errors?

Best regards,
Philipp

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