Composite relaxed extragradient method for triple hierarchical variational inequalities with constraints of systems of variational inequalities

Volume 10, Issue 4, pp 2018--2039 http://dx.doi.org/10.22436/jnsa.010.04.58

Publication Date: April 20, 2017 Submission Date: January 10, 2017

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Authors

Lu-Chuan Ceng - Department of Mathematics, Shanghai Normal University; and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, China. Yeong-Cheng Liou - Department of Healthcare Administration and Medical Informatics, and Research Center of Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 807, Taiwan. - Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung 807, Taiwan. Ching-Feng Wen - Center for General Education; and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 807, Taiwan.

Abstract

In this paper, we introduce and analyze a composite relaxed extragradient viscosity algorithm for solving the triple hierarchical variational inequality problem with the constraint of general system of variational inequalities in a real Hilbert space. Strong convergence of the iteration sequences generated by the algorithm is established under some suitable conditions. Our results improve and extend the corresponding results in the earlier and recent literature.

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Keywords

• Composite relaxed extragradient algorithm
• triple hierarchical variational inequality
• general system of variational inequalities
• inverse-strongly monotone mapping.

MSC

•  49J30
•  47H09
•  47J20
•  49M05

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