An inertial subgradient extragradient method of variational inequality problems involving quasi‐nonexpansive operators with applications. (15th July 2021)

• Record Type: Journal Article
• Authors: Suparatulatorn, Raweerote; Charoensawan, Phakdi; Khemphet, Anchalee
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 17(2021)
• Page Start: 13526
• Page End: 13539
• Publication Date: 2021-07-15
• Subjects: compressed sensing -- fixed point -- inertial method -- subgradient extragradient method -- variational inequality; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7641
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this work, a new algorithm is suggested to solve the variational inequality problems for Lipschitz continuous and monotone operators and the fixed point problems for quasi‐nonexpansive operators. This algorithm is constructed based on the inertial subgradient extragradient method. In addition, a strong convergence theorem for this algorithm is obtained under some extra conditions. Furthermore, an application to a signal recovery in compressed sensing problem is shown as a numerical example of the algorithm. Additionally, another example in an infinite‐dimensional space is given.