Block-proximal methods with spatially adapted acceleration

We study and develop (stochastic) primal–dual block-coordinate descent methods based on the method of Chambolle and Pock. Our methods have known convergence rates for the iterates and the ergodic gap: O(1/N 2) if each each block is strongly convex, O(1/N ) if no convexity is present, and more generally a mixed rate O(1/N 2) + O(1/N ) 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 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. Get the version from h p://tuomov.iki.fi/publications/, citations may be broken in this one due arXiv’s inability to support biblatex.