Hi Philippe,
Is your problem to min_{a,b,c} f(a,b,c) s.t. a+b+c=1 for f:R^3 -> R? Do you
mean your function is non-Euclidean because it is mapping to some space other
than R?
Perhaps more concretely explaining your problem would help.
Best,
Grey
> On Jan 25, 2017, at 11:18 AM, philippe preux <philippe.pr...@inria.fr> wrote:
>
> Hi,
> I am optimizing a differentiable function defined over a probability
> distribution. That is, say the function to optimize has 3 parameters a, b and
> c each being a probability and such that a + b + c = 1.
> We know that optimizing each parameter independently from the other 2 is not
> the best way to go as we do not take the a+b+c=1 constraint into
> consideration. The solution is not to add this constraint to the problem via
> an equality constraint; the issue is that the space is not Euclidian and that
> whenever one computes the gradient wrt to a parameter (say a), the 2 others
> should also be considered, to take the shape of the manifold on which I
> optimize into consideration. It seems to me that directional derivatives, or
> natural gradients are needed here.
> So my question is: how to deal with such non Euclidian spaces with nlopt?
> Thanks for any help,
> Philippe
>
>
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