# [Ipopt] optimization with experimental data

Ruhollah Tavakoli rohtav at gmail.com
Wed Jun 16 03:56:59 EDT 2010

```Hi,

note that your problem is very simple unconstrained optimization which is
easy to solve just using a 2x2 matrix inversion!

For a good reference on the topic read chapter 6 of this famous online book:
http://www.stanford.edu/~boyd/cvxbook/

or simply read example 3 in chapter 8 of
Burden & Faires, Numerical analysis, 7ed. which is identical to your problem
(I usually assign, like it, as a homework in undergraduate sci. comp.
course).

hope this helps

RT

On Tue, Jun 15, 2010 at 1:23 AM, <pierre-lin.pommier at fr.michelin.com> wrote:

>
> Hello,
>
> I'm looking for to solve an optimization problem. I have some experimental
> data and I want to minimize the difference (L2-norm) between the model and
> the measures.
>
> I have some difficulties to link Ipopt solver : how can I take into account
> these experimental data in functions "eval_f", "eval_grad_f", "eval_g",
> "eval_jac_g" and "eval_h" ?
>
> You gave an example to minimize a function without experimental data.
>
> For instance, if my function is
>
> y(p1, p2, x) = p1 * exp(p2 * x)
>
> where p1 and p2 are my 2 parameters, x is my variable (the temperature for
> instance). So at each componant of x, called x_i, I must have a new point
> y(p1, p2, x_i)
>
> the jacobian of my function is
>
> exp(p2 * x)
> p2 * p1 * exp(p2 * x)
>
> for each x.
>
> How can I program functions "eval_f", "eval_grad_f", "eval_g", "eval_jac_g"
> and "eval_h" ?
>
> Thank you very much.
>
> Sincerly,
>
> Pierre-Lin Pommier
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