Proximal gradient method: Difference between revisions

Revision as of 05:08, 17 November 2016

Revision as of 05:21, 17 November 2016

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== Definition ==

ProximityThe operatorsproximity operator of a convex function <math>f</math> at <math>x</math> is defined as the unique solution to

For every <math>x \in \mathbb{R}^N </math>, the minimization problem

:<math>

\text{minimize}_{y \in C} \qquad f(y) + \frac{1}{2} \left\| x-y \right\|_2^2

</math>

admits a unique solution whichand is denoted by <math>\operatorname{prox}_f(x)</math>.

: <math>