Hybrid inertial subgradient extragradient methods for variational inequalities and fixed point problems involving asymptotically nonexpansive mappings

In this paper, we introduce hybrid inertial subgradient extragradient algorithms with line-search process for solving a variational inequality problem (VIP) with pseudomonotone and Lipschitz continuous mapping and a common fixed-point problem (CFPP) of finitely many nonexpansive mappings and an asym...

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Published inOptimization Vol. 70; no. 4; pp. 715 - 740
Main Authors Ceng, Lu-Chuan, Shang, Meijuan
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 03.04.2021
Taylor & Francis LLC
Subjects
Algorithms
Approximation
Asymptotic methods
Asymptotic properties
asymptotically nonexpansive mapping
common fixed point
Fixed points (mathematics)
Hilbert space
Hybrid inertial subgradient extragradient method
Mapping
pseudomonotone variational inequality
Search process
sequentially weak continuity
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Abstract In this paper, we introduce hybrid inertial subgradient extragradient algorithms with line-search process for solving a variational inequality problem (VIP) with pseudomonotone and Lipschitz continuous mapping and a common fixed-point problem (CFPP) of finitely many nonexpansive mappings and an asymptotically nonexpansive mapping in a real Hilbert space. The proposed algorithms are based on inertial subgradient extragradient method with line-search process, hybrid steepest-descent method, and viscosity approximation method. Under mild conditions, we prove strong convergence of the proposed algorithms to an element in the common solution set of the VIP and CFPP, which solves a certain hierarchical VIP defined on this common solution set.
AbstractList In this paper, we introduce hybrid inertial subgradient extragradient algorithms with line-search process for solving a variational inequality problem (VIP) with pseudomonotone and Lipschitz continuous mapping and a common fixed-point problem (CFPP) of finitely many nonexpansive mappings and an asymptotically nonexpansive mapping in a real Hilbert space. The proposed algorithms are based on inertial subgradient extragradient method with line-search process, hybrid steepest-descent method, and viscosity approximation method. Under mild conditions, we prove strong convergence of the proposed algorithms to an element in the common solution set of the VIP and CFPP, which solves a certain hierarchical VIP defined on this common solution set.
Author Ceng, Lu-Chuan
Shang, Meijuan
Author_xml – sequence: 1
  givenname: Lu-Chuan
  surname: Ceng
  fullname: Ceng, Lu-Chuan
  organization: Department of Mathematics, Shanghai Normal University
– sequence: 2
  givenname: Meijuan
  surname: Shang
  fullname: Shang, Meijuan
  email: meijuanshang@163.com
  organization: College of Science, Shijiazhuang University
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Snippet In this paper, we introduce hybrid inertial subgradient extragradient algorithms with line-search process for solving a variational inequality problem (VIP)...
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SubjectTerms Algorithms
Approximation
Asymptotic methods
Asymptotic properties
asymptotically nonexpansive mapping
common fixed point
Fixed points (mathematics)
Hilbert space
Hybrid inertial subgradient extragradient method
Mapping
pseudomonotone variational inequality
Search process
sequentially weak continuity
Title Hybrid inertial subgradient extragradient methods for variational inequalities and fixed point problems involving asymptotically nonexpansive mappings
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