ما معنى Proximal operator, proximal gradient method؟

The proximal operator of a convex function $g$ is $\operatorname{prox}_{tg}(v) = \arg\min_x\bigl(g(x) + \frac1{2t}\lVert x - v\rVert^2\bigr)$; for $g = \lambda\lVert\cdot\rVert_1$ it is soft thresholding. The proximal gradient method minimises $f + g$, $f$ smooth, by $x_{k+1} = \operatorname{prox}_{g/L}(x_k - \nabla f(x_k)/L)$; FISTA (Beck and Teboulle, 2009) adds Nesterov’s extrapolation.