A modified subgradient extragradient method with non-monotonic step sizes for solving quasimonotone variational inequalities

In this work, we propose a self-adaptive projection method for solving variational inequalities with Lipschitz continuous and quasimonotone mapping (or Lipschitz continuous mapping without monotonicity) in real Hilbert space. Using the technique of double inertial steps into a single projection meth...

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Bibliographic Details
Published in:	Computational & applied mathematics Vol. 43; no. 4
Main Authors:	Thong, Duong Viet, Li, Xiao-Huan, Dung, Vu Tien, Van Thang, Hoang, Van Long, Luong
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01-06-2024 Springer Nature B.V
Subjects:	Algorithms Applications of Mathematics Computational Mathematics and Numerical Analysis Hilbert space Inequalities Mapping Mathematical Applications in Computer Science Mathematical Applications in the Physical Sciences Mathematics Mathematics and Statistics 65K15 47J20 linear convergence rate Quasimonotone mapping 90C25 47H09 Quasimonotone variational inequality Non-monotone mapping Lipschitz continuity
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Summary:	In this work, we propose a self-adaptive projection method for solving variational inequalities with Lipschitz continuous and quasimonotone mapping (or Lipschitz continuous mapping without monotonicity) in real Hilbert space. Using the technique of double inertial steps into a single projection method, we give weak and strong convergence theorems of the proposed algorithm. The results obtained in this paper extend some recent results in the literature.
ISSN:	2238-3603 1807-0302
DOI:	10.1007/s40314-024-02699-2