Proximal Operator of a Composition of Functions

Asked Jul 27 '17 at 20:12

Active Mar 16 '20 at 16:10

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Is there a way to compute the proximal operator for the composition of two functions $f \circ g(x)$ using $\mathrm{prox}_{f}$ and $\mathrm{prox}_{g}$? If $g(x) = A x$ is a semi-orthogonal linear map ($A A^* = I$), one has

$$ \mathrm{prox}_{f \circ A}(x) = A^*\ \mathrm{prox}_{f}(A x). $$

Is there a similar result for weaker conditions on $g(x)$?

edited Mar 16 '20 at 16:10

Royi

8,711

asked Jul 27 '17 at 20:12

pratikac

I doubt you'll get very far with anything nonlinear. Linear/affine, perhaps. – Michael Grant Jul 28 '17 at 13:47
I agree with @MichaelGrant that all bets are probably off. – dohmatob Jul 28 '17 at 21:33
Hmm, thanks though :) – pratikac Jul 29 '17 at 00:00
Have a look at - https://math.stackexchange.com/a/3310302/33. – Royi Mar 15 '20 at 20:28

Proximal Operator of a Composition of Functions

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