A new modified two-subgradient extragradient algorithm for solving variational inequality problems
Received:July 04, 2021  Revised:December 01, 2021
Key Word: Two-subgradient extragradient algorithm, monotone, Lipschitz continuous, variational inequality, Hilbert space  
Fund ProjectL:National Natural Science Foundation of China (No.11871059), National Natural Science Foundation of China (No. 11801455), Sichuan Science and Technology Program (No. 2019YFG0299) and supported by the Talent Research Fund Project of China West Normal University (No. 17YC394).
Author NameAffiliationAddress
Jia-xin Chen College of Mathematical Sciences, Sichuan Normal University 成都市锦江区静安路5号 (邮编:610068)
Minglu Ye School of mathematics and information, China West Normal University 四川省南充市顺庆区师大路1号华凤校区数学与信息学院(邮编:637002)
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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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