Hybrid extragradient method for hierarchical variational inequalities

DOI10.1186/1687-1812-2014-222zbMath1376.49008OpenAlexW2104243281WikidataQ59324524 ScholiaQ59324524MaRDI QIDQ2406157

Abdul Latif, Jen-Chih Yao, Qamrul Hasan Ansari, Lu-Chuan Ceng

Publication date: 26 September 2017

Published in: Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-1812-2014-222

zbMATH Keywords

nonexpansive mappingsvariational inclusionsgeneralized mixed equilibrium problemhierarchical variational inequalitiesgeneral system of variational inequalitiesstrictly pseudocontractive mappingsmultistep hybrid extragradient algorithm

Mathematics Subject Classification ID

Variational and other types of inequalities involving nonlinear operators (general) (47J20) Variational inequalities (49J40) Newton-type methods (49M15) Hierarchical systems (93A13) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49J30)

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Relaxed extragradient methods for systems of variational inequalities ⋮ On general implicit hybrid iteration method for triple hierarchical variational inequalities with hierarchical variational inequality constraints ⋮ Hybrid steepest-descent methods for triple hierarchical variational inequalities ⋮ A hybrid iterative method for common solutions of variational inequality problems and fixed point problems for single-valued and multi-valued mappings with applications ⋮ A subgradient proximal method for solving a class of monotone multivalued variational inequality problems ⋮ Hybrid inertial subgradient extragradient methods for variational inequalities and fixed point problems involving asymptotically nonexpansive mappings ⋮ Systems of variational inequalities with hierarchical variational inequality constraints for asymptotically nonexpansive and pseudocontractive mappings ⋮ New subgradient extragradient methods for solving monotone bilevel equilibrium problems ⋮ Triple-hierarchical problems with variational inequality ⋮ Hybrid extragradient viscosity method for general system of variational inequalities ⋮ Implicit and explicit iterative methods for mixed equilibria with constraints of system of generalized equilibria and hierarchical fixed point problem

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