Proximal operator

In mathematical optimization, the proximal operator is an operator associated with a convex function $f$ defined by:

$\operatorname {prox} _{f}(v)=\operatorname {argmin} \limits _{x}\left(f(x)+{\frac {1}{2}}\|x-v\|_{2}^{2}\right).$

It is frequently used in optimization algorithms associated with non-differentiable optimization problems such as total variation denoising.

See also

• Proximal gradient method