Two adaptive modified subgradient extragradient methods for bilevel pseudomonotone variational inequalities with applications
- Tan, Bing; Cho, Sun Young
- Issue Date
- Bilevel variational inequality; Inertial method; Extragradient method; Adaptive stepsize; Pseudomonotone operator
- COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v.107
- Journal Title
- COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
- We consider the bilevel variational inequality problem with a pseudomonotone operator in real Hilbert spaces and investigate two modified subgradient extragradient methods with inertial terms. Our first scheme requires the operator to be Lipschitz continuous (the Lipschitz constant does not need to be known) while the second one only requires it to be uniformly continuous. The proposed methods employ two adaptive stepsizes making them work without the prior knowledge of the Lipschitz constant of the mapping. The strong convergence properties of the iterative sequences generated by the proposed algorithms are obtained under mild conditions. Some numerical tests and applications are given to demonstrate the advantages and efficiency of the stated schemes over previously known ones. (C) 2021 Elsevier B.V. All rights reserved.
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- 본부대학II > 휴먼헬스케어학과 > Journal Articles
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