Three-step projected forward–backward algorithms for constrained minimization problem

We design new projective forward–backward algorithms for constrained minimization problems. We then discuss its weak convergence via a new linesearch that the hypothesis on the Lipschitz constant of the gradient of functions is avoided. We provide its applications to solve image deblurring and image...

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Bibliographic Details
Published inJournal of applied mathematics & computing Vol. 71; no. 1; pp. 465 - 487
Main Authors Kankam, Kunrada, Noor, Muhammad Aslam, Cholamjiak, Prasit
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Nature B.V 01.02.2025
Subjects
Algorithms
Constraints
Hilbert space
Lipschitz condition
Optimization
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ISSN1598-5865
1865-2085
DOI10.1007/s12190-024-02248-4

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Summary:We design new projective forward–backward algorithms for constrained minimization problems. We then discuss its weak convergence via a new linesearch that the hypothesis on the Lipschitz constant of the gradient of functions is avoided. We provide its applications to solve image deblurring and image inpainting. Finally, we discuss the optimal selection of parameters that are proposed in algorithms in terms of PSNR and SSIM. It reveals that our new algorithm outperforms some recent methods introduced in the literature.
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ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-024-02248-4