Weak convergence of projection algorithm with momentum terms and new step size rule for quasimonotone variational inequalities
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910935291002880 |
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| author | Kumar, Gourav Soe, Santanu Vetrivel, V. |
| author_facet | Kumar, Gourav Soe, Santanu Vetrivel, V. |
| contents | This article analyses the simple projection method proposed by Izuchukwu et al. [8, Algorithm 3.2] for solving variational inequality problems by incorporating momentum terms. A new step size strategy is also introduced, in which the step size sequence increases after a finite number of iterations. Under the assumptions that the underlying operator is quasimonotone and Lipschitz continuous, we establish weak convergence of the proposed method. The effectiveness and efficiency of the algorithm are demonstrated through numerical experiments and are compared with existing approaches from the literature. Finally, we apply the proposed algorithm to a signal recovery problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06170 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak convergence of projection algorithm with momentum terms and new step size rule for quasimonotone variational inequalities Kumar, Gourav Soe, Santanu Vetrivel, V. Optimization and Control 47J20, 49J40, 65K15, 65Y20 This article analyses the simple projection method proposed by Izuchukwu et al. [8, Algorithm 3.2] for solving variational inequality problems by incorporating momentum terms. A new step size strategy is also introduced, in which the step size sequence increases after a finite number of iterations. Under the assumptions that the underlying operator is quasimonotone and Lipschitz continuous, we establish weak convergence of the proposed method. The effectiveness and efficiency of the algorithm are demonstrated through numerical experiments and are compared with existing approaches from the literature. Finally, we apply the proposed algorithm to a signal recovery problem. |
| title | Weak convergence of projection algorithm with momentum terms and new step size rule for quasimonotone variational inequalities |
| topic | Optimization and Control 47J20, 49J40, 65K15, 65Y20 |
| url | https://arxiv.org/abs/2505.06170 |