Systems of variational inequalities with hierarchical variational inequality constraints for Lipschitzian pseudocontractions
By Lu-Chuan Ceng, Adrian Petrusel, Jen-Chih Yao, Yonghong Yao. Fixed Point Theory, 2019
81 citations recorded by the source corpus.
In this paper, we consider the problem of solving a general system of variational inequalities (GSVI) with a hierarchical variational inequality (HVI) constraint for countably many uniformly Lipschitzian pseudocontractive mappings and an accretive operator in a real Banach space. We propose an implicit composite extragradient-like method based on the Mann iteration method, the viscosity approximation method and the Korpelevich extragradient method. Convergence results for the proposed iteration method are also established under some suitable assumptions.
Subfields: Civil and Structural Engineering, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/5eb78dc622b858b9a8277ff8273f10be7f4791ec
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Citations in the corpus
- A monotone Bregan projection algorithm for fixed point and equilibrium problems in a reflexive Banach space (2020, background): “In view of the generality and importance of equilibrium problems, fixed point algorithms have been extensively investigated for approximation solutions of problem (1); see [1, 7, 14, 23, 27, 33] and the references therein.”