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I am really confused about the proximal operator. My teacher has lectured and posted notes where she defines the proximal operator like this:

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I am trying to get some intuition for this weird function. What is the variable $\xi$ supposed to represent? I know there is some notion where this is supposed to generalize projection?

So naturally I try to look up some other resources. But when I look up the proximal mapping on the internet people have a different definition. For example here:

What Is the Motivation of Proximal Mapping / Proximal Operator?

Are these definitions somehow the same? Can someone help me out of this mess?

Karagounis Z
  • 578

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