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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.


Other associated files : ochs_iAM_arXiv2017.pdf [668KB]  

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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"
}

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