ott.geometry.regularizers.Regularization.moreau_envelope

ott.geometry.regularizers.Regularization.moreau_envelope#

Regularization.moreau_envelope(x, tau=1.0)#

Moreau Envelope.

Uses Remark 12.24 from [Bauschke and Combettes, 2017]:

\[{^\tau}f\left(x\right) = f\left(\prox_{\tau f}\left(x\right)\right) + \frac{1}{2\tau}\|x - \prox_{\tau f}\left(x\right)|_2^2\]
Parameters:
  • x (Array) – Array of shape [d,].

  • tau (float) – Positive weight.

Return type:

Array

Returns:

The Moreau Envelope of x.