[Coin-ipopt] pb with discontinuity of Hessian

[Andreas Waechter]

Hi Sylvain,

I personally don't have any experience how Ipopt behaves when the problem 
has non-continuous Hessians.  From a theoretical point of view, global 
convergence should not be endangered (but, as I guess we all know, theory 
and practice can sometimes differ widely... :).  What probably matters 
much more is how nonlinear the functions are, whether you have 
degeneracies, and how well your problem is scaled.

As for local convergence, this might depend on how bad the noncontinuities 
are, and whether the optimum is at or close such a discontinuous point. 
You could of course also use the quasi-Newton approximation of the 
Lagrangina Hessian, but I would expect that to be much worse, unless your 
discontinuities are really bad.

If it is easy for you to try, I would suggest to just go ahead and see how 
Ipopt does (I would be interested to know).

Anybody else any idea?

Thanks

Andreas

On Tue, 13 Mar 2007, Sylvain Miossec wrote:

> Hi,
>
> I have an optimization problem with continuous criteria and constraints 
> gradients, continuous criteria hessian but discontinuous constraints 
> hessians. I saw in an IPOPT paper that the conditions of use of IPOPT are 
> that criteria and constraints are twice differentiable.
> I would like to have an idea of the implications of the absence of twice 
> differentiability for my problem. From a theoretical point of view is this 
> twice differentiability is absolutely necessary to the convergence proof, or 
> just for the quadratic convergence proof ? Then in a practical 
> implementation, can IPOPT converge slowly ? Would it be better to smooth the 
> constraints so that they are twice differentiable (which seems to be not that 
> easy) ?
>
> Any information about this would help me a lot.
>
> Sylvain
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