Proximal gradient method
= Proximal gradient method
The proximal gradient method minimizes $g+h$, where $g$ has an $L$-Lipschitz gradient and $h$ is convex with a tractable <proximal operator>, by $x_{r+1}=\operatorname{prox}_{\alpha h}(x_r-\alpha\nabla g(x_r))$. A standard choice $0<\alpha\leq1/L$ gives objective error $O(1/r)$ in the general convex case.
This basic forward-backward update is one of the <proximal gradient methods for learning>.