20 research outputs found
Block-proximal methods with spatially adapted acceleration
We study and develop (stochastic) primal--dual block-coordinate descent
methods for convex problems based on the method due to Chambolle and Pock. Our
methods have known convergence rates for the iterates and the ergodic gap:
if each block is strongly convex, if no convexity is
present, and more generally a mixed rate for strongly convex
blocks, if only some blocks are strongly convex. Additional novelties of our
methods include blockwise-adapted step lengths and acceleration, as well as the
ability to update both the primal and dual variables randomly in blocks under a
very light compatibility condition. In other words, these variants of our
methods are doubly-stochastic. We test the proposed methods on various image
processing problems, where we employ pixelwise-adapted acceleration