Papers › Block-proximal methods with spatially adapted acceleration
Block-proximal methods with spatially adapted acceleration
Tuomo Valkonen
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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: O(1/N²) if each block is strongly convex, O(1/N) if no convexity is present, and more generally a mixed rate O(1/N²)+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 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.
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