# Tag Info

Our goal is to obtain proximal operator of the following function $$g \left( x \right) = {\left\| x \right\|}_{1} + \operatorname{TV}(x).$$ The involved optimization problem for any $z \in \mathbb{R}^d$ is the following $$\text{argmin}_{x}\left\{g(x) + \frac{1}{2}\|x-z\|^2_2\right\}$$ Denote the following $$g_1(x) := {\left\| x \right\|}_{1} + \frac{1}... 3 Indeed the model for the Proximal Gradient Method (Also see Proximal Gradient Methods for Learning) is in the form of:$$ F \left( x \right) = f \left( x \right) + g \left( x \right)  Where usually $f \left( x \right)$ is convex smooth function and $g \left( x \right)$ is convex non smooth function. Yet the model is quite flexible and you may define ...