Proximal gradient method: Difference between revisions

Revision as of 11:15, 21 November 2013

Revision as of 19:50, 25 November 2013

Line 76:

<math>

\begin{align}

& minimize_\text{minimize}_{y \in C} & f(y) + \frac{1}{2} \parallel x-y \parallel_2^2 &

\end{align}

</math>

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

<math>

prox_f\operatorname{prox}_f(x) :\mathbb{R}^N \rightarrow \mathbb{R}^N

</math>

Line 89:

<math>

\begin{align}

& p=prox_f\operatorname{prox}_f(x) \Leftrightarrow x-p \in \partial f(p) & (\forall(x,p) \in \mathbb{R}^N \times \mathbb{R}^N)

\end{align}

</math>

Line 97:

<math>

\begin{align}

& p=prox_f\operatorname{prox}_f(x) \Leftrightarrow x-p \in \triangledown f(p) & (\forall(x,p) \in \mathbb{R}^N \times \mathbb{R}^N)

\end{align}

</math>