[Ipopt] Can IPOPT do this

[Andreas Waechter]

Hi Ned,

I'm copying your email to the Ipopt mailing list - in general, it might be 
a good idea to send questions like this one there, since other people 
might have better ideas then me...

No, Ipopt cannot deal with the situation you describe, it requires 
functions that are at least once continuously differentiable.  Otherwise, 
it might get stuck.

You can look at methods for non-smooth optimization, or you can maybe 
model your problem as an MINLP.  If the resulting problem formulation is 
convex (unlikely, since your have equality constraints, unless you can 
relax them), you can use method like Bonmin or FilMINT, otherwise there 
are a number of global optimization codes, such as BARON, Lago, or 
Couenne.  (Bonmin, Couenne, and Lago are available on COIN.)

Regards,

Andreas

On Mon, 8 Jun 2009, Ned Nedialkov wrote:

>
>
> Hi Andreas,
>
> I need to minimize a function subject to constraints that are not 
> differentiable everywhere.
> That is, my constraint function is generally of the sort
>
> 	if (some condition on x_i's)
> 	   F_1(x_1, ..., x_n) = 0
> 	else
> 	   F_2(x_1, ..., x_n)  = 0
>
> where I can provide Jacobians for F_1 and F_2. My objective is simple, min 
> ||x-a||_2^2.
>
> I am wondering if the theory behind IPOPT can deal with this. If not, do you 
> have any idea
> what method/software may be applicable.
>
> Many thanks,
> Ned
>
>