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

Yunus Atalan (), Emirhan Hacıoğlu (), Müzeyyen Ertürk (), Faik Gürsoy () and Gradimir V. Milovanović ()
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Yunus Atalan: Aksaray University
Emirhan Hacıoğlu: Trakya University
Müzeyyen Ertürk: Adiyaman University
Faik Gürsoy: Adiyaman University
Gradimir V. Milovanović: Serbian Academy of Sciences and Arts

Journal of Global Optimization, 2024, vol. 90, issue 4, No 3, 869-890

Abstract: Abstract 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.

Keywords: Iterative algorithm; Variational inequalities; Relaxed ( $$\kappa $$ κ; $$\omega $$ ω )-cocoercive mappings; Nonexpansive mappings (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10898-024-01425-w

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