Proximal operator

In mathematical optimization, the proximal operator is an operator associated with a convex function $f$ defined by:^[1]

\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

References

↑ Neal Parikh. "Proximal Algorithms" (PDF). Web.stanford.edu. Retrieved 2016-09-25.

External links

The Proximity Operator repository: a collection of proximity operators implemented in Matlab and Python.
ProximalOperators.jl: a Julia package implementing proximal operators.
ODL: a Python library for inverse problems that utilizes proximal operators.

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