A New Modified Two-Subgradient Extragradient Algorithm for Solving Variational Inequality Problems
Received:July 04, 2021  Revised:December 23, 2021
Key Words: two-subgradient extragradient algorithm   monotone   Lipschitz continuous   variational inequality   Hilbert space  
Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11871059; 11801455), Sichuan Science and Technology Program (Grant No.2019YFG0299) and General Cultivation Program of China West Normal University (Grant No.20A024).
Author NameAffiliation
Jiaxin CHEN School of Mathematical Sciences, Sichuan Normal University, Sichuan 610066, P. R. China 
Minglu YE School of Mathematics and Information, China West Normal University, Sichuan 637002, P. R. China 
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      In this paper, we propose a modified two-subgradient extragradient algorithm (MTSEGA) for solving monotone and Lipschitz continuous variational inequalities with the feasible set being a level set of a smooth convex function in Hilbert space. The advantage of MTSEGA is that all the projections are computed onto a half-space per iteration. Moreover, MTSEGA only needs one computation of the underlying mapping per iteration. Under the same assumptions with the known algorithm, we show that the sequence generated by this algorithm is weakly convergent to a solution of the concerned problem.
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