Machine Learning

8.13 Proximal Operators

So far in the chapter, we have devoted a lot of space to the notion of the projection operator. In this section, we go one step further and we will introduce an elegant generalization of the notion of projection. Just to establish a clear understanding, when we refer to an operator, we mean a mapping from ^ll, in contrast to a function which is a mapping ^l.

Definition 8.9

Let

$f:{ℝ}^l\mapsto ℝ,$

be a convex function and λ > 0. The ...