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arXiv · 2604.07241

Non-Lipschitz Inertial Contraction-Type Method for Monotone Variational Inclusion problems

Feeroz Babu·Syed Shakaib Irfan·Jen-Chih Yao·Xiaopeng Zhao
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Abstract

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.

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Feeroz Babu, Syed Shakaib Irfan, Jen-Chih Yao, Xiaopeng Zhao. 2026-04-08. Non-Lipschitz Inertial Contraction-Type Method for Monotone Variational Inclusion problems. https://arxiv.org/abs/2604.07241

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