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Conference papers

Local Linear Convergence of Inertial Forward-Backward Splitting for Low Complexity Regularization

Abstract : In this abstract, we consider the inertial Forward-Backward (iFB) splitting method and its special cases (Forward-Backward/ISTA and FISTA). Under the assumption that the non-smooth part of the objective is partly smooth relative to an active smooth manifold, we show that iFB-type methods (i) identify the active manifold in finite time, then (ii) enter a local linear convergence regime that we characterize precisely. This gives a grounded and unified explanation to the typical behaviour that has been observed numerically for many low-complexity regularizers, including 1 , 1,2-norms, total variation (TV) and nuclear norm to name a few. The obtained results are illustrated by concrete examples.
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https://hal-normandie-univ.archives-ouvertes.fr/hal-02456434
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Submitted on : Monday, January 27, 2020 - 1:12:34 PM
Last modification on : Tuesday, January 18, 2022 - 3:23:57 PM

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  • HAL Id : hal-02456434, version 1

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Jingwei Liang, Jalal M. Fadili, Gabriel Peyré. Local Linear Convergence of Inertial Forward-Backward Splitting for Low Complexity Regularization. SPARS, 2015, Cambridge, France. ⟨hal-02456434⟩

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