Ingrid Hallen ingridhallen at hotmail.com
Mon Apr 8 09:38:29 EDT 2013

```Thanks for the suggestions!

Regarding the first, I think it might not be so efficient for my problem, having
almost as many constraints as variables. But I might give it a try. Perhaps
one can modify the code for sparse_hess in some clever way ...

Regarding the second I am unfortunately clueless as to how one could
exploit that fact.

Kind regards,

Ingrid

Date: Sun, 7 Apr 2013 15:31:50 -0700
From: normvcr at telus.net
Subject: Re: [ADOL-C] Evaluating Hessian of Lagrangian

Perhaps you can trace L as a function
of both x and lambda.

Then when you need the hessian,

calculate the hessian only with respect to x.

Not sure if this is better/worse than what you suggested.

When using the Hessian of the Lagrangian, you will eventually be
restricting

attention to the kernel of your constraints.  Do you know if this
fact

would offer a simplification to how the hessian could be computed?

Norm

On 04/05/2013 04:02 AM, Ingrid Hallen wrote:

Hi,

I'm doing non-linear optimization with IPOPT. For this, I'm

to compute the Hessian of the Lagrangian

L(x,lambda) = f(x) + sum_{i}lambda_{i}h_{i}(x),

where x are the variables, lambda the Lagrange multipliers and

f(x) and h_{i}(x) objective and constraint functions.

What I'm doing in my code is the following (omitting details):

// **********************

// Trace Lagrangian function

trace_on(tag);

for(i=0;i<n;i++) {

}

trace_off();

// Evaluate Hessian of the Lagrangian

repeat = 0;

sparse_hess(tag,n,repeat,x,&nnz,&rind,&cind,&values,&options)

// ***********************

This works fine, but is not so efficient. One reason is that,
since lambda changes,

the Lagrangian function has to be retaped every time the Hessian
is needed and so it

appears that I cannot set repeat = 1 when calling sparse_hess.

One way to circumvent this problem could perhaps be to trace the
objective

and constraint functions individually and then construct the
Hessian of

the Lagrangian using multiple calls to sparse_hess, but is there
a

more convenient way to do it?

Sincerely,

Ingrid

_______________________________________________

_______________________________________________
-------------- next part --------------
An HTML attachment was scrubbed...
```