Recently, I try to learn Forward backward splitting algorithm.
I find it was proposed in 1988 'Applications of a Splitting Algorithm to Decomposition in Convex Programming and Variational Inequalities'.
It is to minimize $$f(x)+g(x)$$
by two steps, $f(x) $ and $g(x)$ are convex functions, but not necessarily smooth.
$$x_{t+1}=arg\min_u\left\{\frac{1}{2}\|u-(w_t-\nabla t \partial f(w_t)\|^2+\nabla tg(u)) \right\}$$
I want to know the best choice for $\nabla t$ so far. Thank you.