cr.sparse.opt.prox_zero

cr.sparse.opt.prox_zero()

Returns a prox-capable wrapper for the function $f(x)=0$

Returns

A prox-capable function

Return type

ProxCapable

The function $f(x)=0$ is the indicator function for the vector space ${\mathbb{R}}^n$.

The proximal operator

(1)$$p_f(x,t)=\text{arg}\underset{z\in {\mathbb{R}}^n}{min}f(x)+\frac{1}{2t}\Vert z-x{\Vert }_2^2$$

reduces to:

(2)$$p_f(x,t)=\text{arg}\underset{z\in {\mathbb{R}}^n}{min}\frac{1}{2t}\Vert z-x{\Vert }_2^2=x$$