Convergence of the forward-backward algorithm: beyond the worst-case with the help of geometry

We provide a comprehensive study of the convergence of the forward-backward algorithm under suitable geometric conditions, such as conditioning or Łojasiewicz properties. These geometrical notions are usually local by nature, and may fail to describe the fine geometry of objective functions relevant...

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Bibliographic Details
Published in:	Mathematical programming Vol. 198; no. 1; pp. 937 - 996
Main Authors:	Garrigos, Guillaume, Rosasco, Lorenzo, Villa, Silvia
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2023 Springer Springer Verlag
Subjects:	Algorithms Analysis Calculus of Variations and Optimal Control; Optimization Combinatorics Full Length Paper Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Optimization and Control Signal processing Theoretical Inverse problems 90C25 Convergence rates Łojasiewicz property 65K10 49M27 Forward Backward algorithm 47J26 Conditioned functions Source condition
ISSN:	0025-5610, 1436-4646
Online Access:	Get full text
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