New inertial forward–backward algorithm for convex minimization with applications

In this work, we present a new proximal gradient algorithm based on Tseng’s extragradient method and an inertial technique to solve the convex minimization problem in real Hilbert spaces. Using the stepsize rules, the selection of the Lipschitz constant of the gradient of functions is avoided. We th...

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Bibliographic Details
Published in:	Demonstratio mathematica Vol. 56; no. 1; pp. 1168 - 1200
Main Authors:	Kankam, Kunrada, Cholamjiak, Watcharaporn, Cholamjiak, Prasit
Format:	Journal Article
Language:	English
Published:	De Gruyter 15.02.2023
Subjects:	65K05 90C25 90C30 image recovery inertial technique minimization problem Tseng’s extragradient method
ISSN:	2391-4661, 2391-4661
Online Access:	Get full text
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Summary:	In this work, we present a new proximal gradient algorithm based on Tseng’s extragradient method and an inertial technique to solve the convex minimization problem in real Hilbert spaces. Using the stepsize rules, the selection of the Lipschitz constant of the gradient of functions is avoided. We then prove the weak convergence theorem and present the numerical experiments for image recovery. The comparative results show that the proposed algorithm has better efficiency than other methods.
ISSN:	2391-4661 2391-4661
DOI:	10.1515/dema-2022-0188