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

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If you have a question about this talk, please contact Carola-Bibiane Schoenlieb.

Joint CIA-CCIMI seminar

In this talk, a local convergence result for abstract descent methods in non-convex optimization is presented. In particular, the analysis is tailored to inertial methods. The result can be summarized as follows: The sequence of iterates is attracted by a local (or global) minimum, stays in its neighborhood and converges within this neighborhood. This result allows algorithms to exploit local properties of the objective function. Moreover, it reveals an equivalence between iPiano (a generalization of the Heavy-ball method) and inertial averaged/alternating proximal minimization and projection methods. Key for this equivalence is the attraction to a local minimum within a common neighborhood and the fact that, for a prox-regular function, the gradient of the Moreau envelope is locally Lipschitz continuous and expressible in terms of the proximal mapping. In a numerical feasibility problem, the inertial alternating projection method significantly outperforms its non-inertial variants.

This talk is part of the Cambridge Image Analysis Seminars series.

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