Local Convergence of the Heavy-ball Method and iPiano for Non-convex Optimization
Technical Report , arXiv:1606.09070 [math.OC], 2017
Abstract: A local convergence result for abstract descent methods is proved. The sequence of iterates is attracted by a local (or global) minimum, stays in its neighborhood and converges. This result allows algorithms to exploit local properties of the objective function: The gradient of the Moreau envelope of a prox-regular functions is locally Lipschitz continuous and expressible in terms of the proximal mapping. We apply these results to establish relations between an inertial forward-backward splitting method (iPiano) and inertial averaged/alternating proximal minimization.
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BibTex reference
@TechReport{Och17, author = "P. Ochs", title = "Local Convergence of the Heavy-ball Method and iPiano for Non-convex Optimization", institution = "arXiv:1606.09070 [math.OC]", month = " ", year = "2017", url = "http://lmb.informatik.uni-freiburg.de/Publications/2017/Och17" }