proximal: Nonlinear Function
Created: July 07, 2022
Modified: July 07, 2022

proximal

This page is from my personal notes, and has not been specifically reviewed for public consumption. It might be incomplete, wrong, outdated, or stupid. Caveat lector.

Proximal methods in optimization

The proximal operator of a convex function ff is defined as the minimizer of ff plus a distance penalty from a specified point vv:

proxf(v)=argminxf(x)+xv22\text{prox}_f(v) = \arg\min_x f(x) + \|x - v\|_2^2