Modified subgradient extragradient method to solve variational inequalities
Authors
Kanikar Muangchoo
 Faculty of Science and Technology, Rajamangala University of Technology Phra Nakhon (RMUTP), 1381 Pracharat 1 Road, Wongsawang, Bang Sue, Bangkok 10800, Thailand.
Abstract
In this paper, we introduce a new method to solve pseudomonotone variational inequalities with the Lipschitz condition in a real Hilbert space. This problem is a general mathematical problem in the sense that it unifies a number of the mathematical problems as a particular case, such as the optimization problems, the equilibrium problems, the fixed point problems, the saddle point problems and Nash equilibrium point problems. The new method is constructed around two methods: the extragradient method and the inertial method. The proposed method uses a new stepsize rule based on local operator information rather than its Lipschitz constant or any other line search method. The proposed method does not require any knowledge of the Lipschitz constant of an operator. The strong convergence of the proposed method is wellestablished. Finally, we conduct a number of numerical experiments to determine the performance and superiority of the proposed method.
Share and Cite
ISRP Style
Kanikar Muangchoo, Modified subgradient extragradient method to solve variational inequalities, Journal of Mathematics and Computer Science, 25 (2022), no. 2, 133149
AMA Style
Muangchoo Kanikar, Modified subgradient extragradient method to solve variational inequalities. J Math Comput SCIJM. (2022); 25(2):133149
Chicago/Turabian Style
Muangchoo, Kanikar. "Modified subgradient extragradient method to solve variational inequalities." Journal of Mathematics and Computer Science, 25, no. 2 (2022): 133149
Keywords
 Variational inequality problem
 subgradient extragradientlike method
 strong convergence result
 Lipschitz continuity
 pseudomonotone mapping
MSC
 65Y05
 65K15
 68W10
 47H05
 47H10
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