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Modified subgradient extragradient algorithms for solving monotone variational inequalities

Jun YangSchool of Mathematics and Information Science, Xianyang Normal University, Xianyang, People's Republic of ChinaHongwei LiuSchool of Mathematics and Statistics, Xidian University, Xi'an, People's Republic of ChinaZexian LiuSchool of Mathematics and Computer Science, Hezhou University, Hezhou, People's Republic of China
2018en
ABI

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In this paper, we introduce two new algorithms for solving classical variational inequalities problem with Lipschitz continuous and monotone mapping in real Hilbert space. We modify the subgradient extragradient methods with a new step size, the convergence of algorithms are established without the knowledge of the Lipschitz constant of the mapping. Finally, some numerical experiments are presented to show the efficiency and advantage of the proposed algorithms.

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