Mathematical Optimization Group, University of Tübingen

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Mathematical Optimization Group

Department of Mathematics, University of Tübingen, Germany

Local Convergence of the Heavy-ball Method and iPiano for Non-convex Optimization

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.



pdf	Bibtex	arXiv

Latest update: 26.01.2018

Citation:
P. Ochs:
Local Convergence of the Heavy-ball Method and iPiano for Non-convex Optimization.

Technical Report, ArXiv e-prints, arXiv:1606.09070 [math.OC], 2016.

Bibtex:
@techreport{Ochs16, title = {Local Convergence of the Heavy-ball Method and iPiano for Non-convex Optimization}, author = {P. Ochs}, year = {2016}, journal = {ArXiv e-prints, arXiv:1606.09070 [math.OC]}, }