Is there a general algorithm for solving $$ \min f(x) + g(x) + h(x) $$ where all three functions are convex and proximable, $f(x)$ is smooth, and $g(x)$ and $h(x)$ are both nonsmooth?
Note that if the problem was just $$ \min f(x) + g(x) $$ then I could use proximal gradient descent.