We study the block-coordinate forward–backward algorithm in which blocks are updated a random and possibly parallel manner, according to arbitrary probabilities. The allows different stepsizes along block-coordinates fully exploit smoothness properties of objective function. In convex case an infinite dimensional setting, we establish almost sure weak convergence iterates asymptotic rate o(1/n)...

Abstract In this paper, we analyse a proximal method based on the idea of forward–backward splitting for sampling from distributions with densities that are not necessarily smooth. particular, study non-asymptotic properties Euler–Maruyama discretization Langevin equation, where envelope is used to deal non-smooth part dynamics. An advantage envelope, when compared widely-used Moreu–Yoshida one...