Block-proximal methods with spatially adapted acceleration. ETNA - Electronic Transactions on Numerical Analysis
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1 mars 2019
- handle: 10670/1.84u345
- issn: 1068-9613
- doi: 10.1553/etna_vol51s15
info:eu-repo/semantics/openAccess
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Tuomo Valkonen, « Block-proximal methods with spatially adapted acceleration. ETNA - Electronic Transactions on Numerical Analysis », Elektronisches Publikationsportal der Österreichischen Akademie der Wissenschafte, ID : 10.1553/etna_vol51s15
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We study and develop (stochastic) primal-dual block-coordinate descentmethods for convex problems based on the method due to Chambolle and Pock.Our methods have known convergence rates for the iterates and the ergodicgap of$O(1/N^2)$ if each block is strongly convex, $O(1/N)$ if no convexity ispresent, 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 lengthsand acceleration as well as the ability to update both the primal and dualvariables randomly in blocks under a very light compatibility condition. Inother words, these variants of our methods are doubly-stochastic.We test the proposed methods on various image processing problems, wherewe employ pixelwise-adapted acceleration.