Non-Lipschitz Inertial Contraction-Type Method for Monotone Variational Inclusion problems
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866908947865141248 |
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| author | Babu, Feeroz Irfan, Syed Shakaib Yao, Jen-Chih Zhao, Xiaopeng |
| author_facet | Babu, Feeroz Irfan, Syed Shakaib Yao, Jen-Chih Zhao, Xiaopeng |
| contents | This study explores an inertial-based contraction-type approach for addressing monotone variational inclusion problems (in short, MVIP) within real Hilbert spaces. Most contraction-type techniques assume Lipschitz continuity and monotonicity or co-coercivity (inverse strongly monotone) of the single-valued operator. However, the key advantage of the proposed method is that it does not rely on the coercivity condition and the Lipschitz continuity for the single-valued operator. A weak convergence result has been achieved for the proposed algorithm with a convergence rate $\mathcal{O}\left(1/\sqrt{k}\right)$. In addition, the maximal and strong monotonicity of the set-valued operator is used to establish a strong convergence result with the linear convergence rate. To demonstrate the effectiveness of our proposed method, we conduct numerical experiments focused on signal recovery problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07241 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-Lipschitz Inertial Contraction-Type Method for Monotone Variational Inclusion problems Babu, Feeroz Irfan, Syed Shakaib Yao, Jen-Chih Zhao, Xiaopeng Optimization and Control Functional Analysis This study explores an inertial-based contraction-type approach for addressing monotone variational inclusion problems (in short, MVIP) within real Hilbert spaces. Most contraction-type techniques assume Lipschitz continuity and monotonicity or co-coercivity (inverse strongly monotone) of the single-valued operator. However, the key advantage of the proposed method is that it does not rely on the coercivity condition and the Lipschitz continuity for the single-valued operator. A weak convergence result has been achieved for the proposed algorithm with a convergence rate $\mathcal{O}\left(1/\sqrt{k}\right)$. In addition, the maximal and strong monotonicity of the set-valued operator is used to establish a strong convergence result with the linear convergence rate. To demonstrate the effectiveness of our proposed method, we conduct numerical experiments focused on signal recovery problems. |
| title | Non-Lipschitz Inertial Contraction-Type Method for Monotone Variational Inclusion problems |
| topic | Optimization and Control Functional Analysis |
| url | https://arxiv.org/abs/2604.07241 |