syfi team mailing list archive

[kent-and@xxxxxxxxx]

> On Sat 2009-04-18 17:32, kent-and@xxxxxxxxx wrote:
>> For the above equation I think there should be only one minimum and so
>> it will head in the right direction. I'm not sure whether it should be
>> quadratic.
>> If it is convex it can have several minium and it may therefore head
>         ^^^^^^^^^
>
> You probably mean "is not convex".
>
>> towards different minima at different times but I didn't think it could
>> head
>> off to infinity (or creating a singular matrix) ?
>
> Convexity is not sufficient to guarantee global convergence, you need a
> minimum to exist (consider exp(x)) and the Jacobian should be Lipshitz
> continuous with J^{-1} bounded.  These conditions are probably satisfied
> for the models you are discussing.
>
> Jed

Right, but isn't there some results that say that if the functional F(u) goes
to infinity when u goes to +/- infinity and the functional is convex. I
probably
need to refresh this stuff.

Anyway, the main point for me was to check that the AD works properly in an
example where I know it should work. And to include non-homogenous Dirichlet
BC. It appears to work in these simple examples.

The SVK and Fung demos do still not work properly, but it might be that we
start with functions to far away. Or there might be a bug...

Kent