A parallel subgradient method extended to variational inequalities involving nonexpansive mappings

In this paper, we propose and analyze the convergence of new iteration methods for finding a common point of the solution set of a class of pseudomonotone variational inequalities and the fixed point set of a finite system of nonexpansive mappings in a real Hilbert space. The idea of this algorithm...

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Vydáno v:Applicable analysis Ročník 99; číslo 16; s. 2776 - 2792
Hlavní autoři: Anh, Pham Ngoc, Hien, Nguyen Duc, Phuong, Ngo Xuan
Médium: Journal Article
Jazyk:angličtina
Vydáno: Abingdon Taylor & Francis 09.12.2020
Taylor & Francis Ltd
Témata:
47 J25
49 J35
65 K10
90 C25
Algorithms
B. Mordukhovich
Convergence
Fixed point
Hilbert space
Inequalities
Iterative methods
nonexpansive mapping
pseudomonotonicity
subgradient projection method
variational inequality
ISSN:0003-6811, 1563-504X
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Abstract In this paper, we propose and analyze the convergence of new iteration methods for finding a common point of the solution set of a class of pseudomonotone variational inequalities and the fixed point set of a finite system of nonexpansive mappings in a real Hilbert space. The idea of this algorithm is to combine the subgradient method with the parallel splitting-up techniques. The main iteration step in the proposed methods uses only one projection and does not require any Lipschitz continuous condition for the cost mapping. The convergent results are also extended to a pseudomonotone equilibrium problem involving a finite system of nonexpansive mappings. Finally, some numerical examples are developed to illustrate the behavior of the new algorithms with respect to existing algorithms.
AbstractList In this paper, we propose and analyze the convergence of new iteration methods for finding a common point of the solution set of a class of pseudomonotone variational inequalities and the fixed point set of a finite system of nonexpansive mappings in a real Hilbert space. The idea of this algorithm is to combine the subgradient method with the parallel splitting-up techniques. The main iteration step in the proposed methods uses only one projection and does not require any Lipschitz continuous condition for the cost mapping. The convergent results are also extended to a pseudomonotone equilibrium problem involving a finite system of nonexpansive mappings. Finally, some numerical examples are developed to illustrate the behavior of the new algorithms with respect to existing algorithms.
Author Anh, Pham Ngoc
Phuong, Ngo Xuan
Hien, Nguyen Duc
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  givenname: Ngo Xuan
  surname: Phuong
  fullname: Phuong, Ngo Xuan
  organization: Department of Mathematics, University of Fire Fighting and Prevention
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SubjectTerms 47 J25
49 J35
65 K10
90 C25
Algorithms
B. Mordukhovich
Convergence
Fixed point
Hilbert space
Inequalities
Iterative methods
nonexpansive mapping
pseudomonotonicity
subgradient projection method
variational inequality
Title A parallel subgradient method extended to variational inequalities involving nonexpansive mappings
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