Novel algorithms based on forward-backward splitting technique: effective methods for regression and classification

In this paper, we introduce two novel forward-backward splitting algorithms (FBSAs) for nonsmooth convex minimization. We provide a thorough convergence analysis, emphasizing the new algorithms and contrasting them with existing ones. Our findings are validated through a numerical example. The pract...

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Published inJournal of global optimization Vol. 90; no. 4; pp. 869 - 890
Main Authors Atalan, Yunus, Hacıoğlu, Emirhan, Ertürk, Müzeyyen, Gürsoy, Faik, Milovanović, Gradimir V.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2024
Springer Nature B.V
Subjects
Algorithms
Classification
Computer Science
Hilbert space
Machine learning
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
Splitting
cocoercive mappings
Iterative algorithm
,
Nonexpansive mappings
Relaxed
Variational inequalities
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Summary:In this paper, we introduce two novel forward-backward splitting algorithms (FBSAs) for nonsmooth convex minimization. We provide a thorough convergence analysis, emphasizing the new algorithms and contrasting them with existing ones. Our findings are validated through a numerical example. The practical utility of these algorithms in real-world applications, including machine learning for tasks such as classification, regression, and image deblurring reveal that these algorithms consistently approach optimal solutions with fewer iterations, highlighting their efficiency in real-world scenarios.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-024-01425-w