| 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
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| 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). |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2022.04.006 |
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