Proximal operator
In mathematical optimization, the proximal operator is an operator associated with a proper, lower-semicontinuous convex function
from a Hilbert space
to, and is defined by:
It is frequently used in optimization algorithms associated with non-differentiable optimization problems such as total variation denoising.
If is the 0- indicator function of a nonempty, closed, convex set, then it is lower-semicontinuous, proper, and convex and is the orthogonal projector onto that set.
