A recent proximal gradient algorithm for convex minimization problem using double inertial extrapolations

In this study, we suggest a new class of forward-backward (FB) algorithms designed to solve convex minimization problems. Our method incorporates a linesearch technique, eliminating the need to choose Lipschitz assumptions explicitly. Additionally, we apply double inertial extrapolations to enhance...

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Bibliographic Details
Published inAIMS mathematics Vol. 9; no. 7; pp. 18841 - 18859
Main Authors Kesornprom, Suparat, Inkrong, Papatsara, Witthayarat, Uamporn, Cholamjiak, Prasit
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2024
Subjects
forward-backward algorithm
inertial extrapolation
minimization problem
weak convergence
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ISSN2473-6988
2473-6988
DOI10.3934/math.2024917

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Summary:In this study, we suggest a new class of forward-backward (FB) algorithms designed to solve convex minimization problems. Our method incorporates a linesearch technique, eliminating the need to choose Lipschitz assumptions explicitly. Additionally, we apply double inertial extrapolations to enhance the algorithm's convergence rate. We establish a weak convergence theorem under some mild conditions. Furthermore, we perform numerical tests, and apply the algorithm to image restoration and data classification as a practical application. The experimental results show our approach's superior performance and effectiveness, surpassing some existing methods in the literature.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2024917