A strongly convergent subgradient extragradient-Halpern method for solving a class of bilevel pseudomonotone variational inequalities

DOI10.1007/s10013-016-0196-9zbMath1380.49047OpenAlexW2344815392MaRDI QIDQ2405476

Tran Viet Anh

Publication date: 25 September 2017

Published in: Vietnam Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10013-016-0196-9

zbMATH Keywords

strong convergencesubgradient extragradient-Halpern methodbilevel pseudomonotone variational inequalities

Mathematics Subject Classification ID

Nonconvex programming, global optimization (90C26) Variational inequalities (49J40) Numerical methods based on nonlinear programming (49M37) Numerical methods for variational inequalities and related problems (65K15)

Related Items

An iterative method for solving the multiple-sets split variational inequality problem ⋮ On Halpern-type sequences with applications in variational inequality problems ⋮ Modified Tseng's extragradient methods with self-adaptive step size for solving bilevel split variational inequality problems ⋮ A parallel method for variational inequalities with the multiple-sets split feasibility problem constraints ⋮ Modified subgradient extragradient methods for solving bilevel split variational inequality problems in Hilbert spaces ⋮ Linesearch methods for bilevel split pseudomonotone variational inequality problems ⋮ Resolvent-Mann-type algorithm for bilevel problems with split feasibility problem constraint ⋮ An algorithm for a class of bilevel split equilibrium problems: application to a differentiated Nash-Cournot model with environmental constraints ⋮ A self-adaptive extragradient-CQ method for a class of bilevel split equilibrium problem with application to Nash Cournot oligopolistic electricity market models ⋮ New explicit extragradient methods for solving a class of bilevel equilibrium problems ⋮ Bilevel Optimization: Theory, Algorithms, Applications and a Bibliography

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An extragradient algorithm for solving bilevel pseudomonotone variational inequalities
• Strong convergence of the Halpern subgradient extragradient method for solving variational inequalities in Hilbert spaces
• Algorithms for a class of bilevel programs involving pseudomonotone variational inequalities
• The subgradient extragradient method for solving variational inequalities in Hilbert space
• The Tikhonov regularization extended to equilibrium problems involving pseudomonotone bifunctions
• Descent methods for monotone equilibrium problems in Banach spaces
• Neural networks for a class of bi-level variational inequalities
• Proximal methods for a class of bilevel monotone equilibrium problems
• Equilibrium problems and variational models. Based on the meeting, Erice, Italy, June 23--July 2, 2000
• Combined relaxation methods for variational inequalities
• Using the Banach contraction principle to implement the proximal point method for multivalued monotone variational inequalities
• Solving two-level variational inequality
• Descent methods for mixed variational inequalities in a Hilbert space.
• On existence and solution methods for strongly pseudomonotone equilibrium problems
• Tikhonov regularization algorithm for pseudomonotone variational inequalities
• Convexly constrained linear inverse problems: iterative least-squares and regularization
• Strong convergence of subgradient extragradient methods for the variational inequality problem in Hilbert space
• Iterative Algorithms for Nonlinear Operators
• Extensions of Korpelevich's extragradient method for the variational inequality problem in Euclidean space
• Stability property of a class of variational inequalities
• A Hybrid Extragradient-Viscosity Method for Monotone Operators and Fixed Point Problems
• Finite-Dimensional Variational Inequalities and Complementarity Problems
• Mathematical Programs with Equilibrium Constraints