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odlgroup / odl

Operator Discretization Library https://odlgroup.github.io/odl/
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Add proximal for other Lp norms #723

Open adler-j opened 7 years ago

adler-j commented 7 years ago

The various Lp norms ahve proximals that are quite well written out in this article:

http://ttic.uchicago.edu/~argyriou/papers/picanest_arxiv.pdf

We could easily add the ||x||_p^p case, which has a closed form expression, and also ||x||_p which can be "found with a simple linesearch".

The ||x||_infty case also has a closed form expression.

kohr-h commented 7 years ago

We could easily add the ||x||_p^p case, which has a closed form expression

This could be added, true, although the expression is not quite in closed form. The inverse of the expression is in closed form. So it will involve a bit of iteration to find the value.

and also ||x||_p which can be "found with a simple linesearch".

I'm skeptical to this before I see a feasible method. In the meantime, we can also try exploring the "identity - projection on ||.||_p' unit ball" route, there should be ways of making that feasible.