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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