Unifying abstract inexact convergence theorems for descent methods and block coordinate variable metric iPiano
Technical Report , arXiv:1602.07283 [math.OC], 2016
Abstract: An abstract convergence theorem for a class of descent method that explicitly models relative errors is proved. The convergence theorem generalizes and unifies several recent abstract convergence theorems, and is applicable to possibly non-smooth and non-convex lower semi-continuous functions that satisfy the Kurdyka-Lojasiewicz inequality, which comprises a huge class of problems. The descent property is measured with respect to a function that is allowed to change along the iterations, which makes block coordinate and variable metric methods amenable to the abstract convergence theorem. As a particular algorithm, the convergence of a block coordinate variable metric version of iPiano (an inertial forward-backward splitting algorithm) is proved. The newly introduced algorithms perform favorable on an inpainting problem with a Mumford-Shah-like regularization from image processing.
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BibTex reference
@TechReport{Och16b, author = "P. Ochs", title = "Unifying abstract inexact convergence theorems for descent methods and block coordinate variable metric iPiano", institution = "arXiv:1602.07283 [math.OC]", month = " ", year = "2016", url = "http://lmb.informatik.uni-freiburg.de/Publications/2016/Och16b" }