Parallel and cyclic hybrid subgradient extragradient methods for variational inequalities

In this paper, we propose two hybrid subgradient extragradient methods for solving common solutions of variational inequalities problems (CSVIP). The first is a parallel algorithm which can be performed simultaneously while the second is a cyclic algorithm which is computed sequentially on each subp...

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Bibliographic Details
Published in:Afrika mathematica Vol. 28; no. 5-6; pp. 677 - 692
Main Author: Hieu, Dang Van
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2017
Springer Nature B.V
Subjects:
Algorithms
Applications of Mathematics
History of Mathematical Sciences
Inequalities
Mathematics
Mathematics and Statistics
Mathematics Education
Numerical methods
Subgradient extragradient method
Parallel algorithm
Cyclic algorithm
65K15
47H10
Hybrid method
Variational inequality
68W10
47H05
65Y05
ISSN:1012-9405, 2190-7668
Online Access:Get full text
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Summary:In this paper, we propose two hybrid subgradient extragradient methods for solving common solutions of variational inequalities problems (CSVIP). The first is a parallel algorithm which can be performed simultaneously while the second is a cyclic algorithm which is computed sequentially on each subproblem in the family. The novelty of this paper is that we have designed the algorithms to develop possible practical numerical methods when the number of subproblems is large. The algorithms can be considered as improvements of some previously known results for CSVIPs. Numerical experiments are also performed to illustrate the efficiency of the proposed algorithms.
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ISSN:1012-9405
2190-7668
DOI:10.1007/s13370-016-0473-5