| Author Name | Affiliation | Postcode | | Xinyi Wei | School of Mathematics and Statistics,Xidian University,Xi''an,Shaanxi Province,
Xidian University,School of Mathematics and Statistics,Xi''an,Shaanxi Province | 710126 | | Hongwei Liu* | School of Mathematics and Statistics,Xidian University,Xi''an,Shaanxi Province,
Xidian University,School of Mathematics and Statistics,Xi''an,Shaanxi Province | 710126 | | Meiying Wang | School of Mathematics and Statistics,Xidian University,Xi''an,Shaanxi Province,
Xidian University,School of Mathematics and Statistics,Xi''an,Shaanxi Province | 710126 |
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| Abstract: |
| In this study, an original projection-based algorithm is proposed to treat a family of variational inequality models defined on a Hilbert space. The method extends Tseng’s extragradient framework by integrating a double inertial mechanism and a relaxation technique. Provided that quasimonotonicity and uniform continuity hold, the sequence yielded by the algorithm is shown to converge weakly. In contrast to previous studies on quasimonotone variational inequality problems, this study requires neither the assumption of Lipschitz continuity for the mapping nor the assumption that the mapping A satisfies Ax≠0. Thus, this study addresses a more general category of quasimonotone variational inequality problems. In the final stage, numerical experiments are conducted to showcase the effectiveness and comparative advantages of the proposed method. |
| Key words: Variational Inequality Problem Projected Gradient Algorithm Quasimonotone Mapping Uniformly Continuous |
| DOI：10.11916/j.issn.1005-9113.25057 |
| Clc Number:47H05 47J20 47J25 65K15 90C25 |
| Fund: |
