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<p>The purpose of this work is to refine the inertial subgradient extragradient algorithm for solving variational inequality problems in real Hilbert spaces. Under the new assumptions, the cost operator does not need any monotonicity. Moreover, the advantage of the proposed algorithm is that the analysis and proof of its weak convergence use self-adaptive step-sizes without requiring the Lipschitz continuity condition and any line-search rules or adding projection onto the feasible subset. The results of this paper provide new insights into non-monotone variational inequality problems and non-Lipschitz continuity, extending and enriching existing results in the literature. Finally, we give numerical experiments to illustrate the effectiveness of our proposed algorithm.</p>

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Convergence analysis of a self-adaptive inertial subgradient extragradient method for non-monotone variational inequalities with non-Lipschitz continuous mappings

  • 期刊论文

  • 发表日期：

    2026年3月3日

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  • Duong Viet Thong

摘要

The purpose of this work is to refine the inertial subgradient extragradient algorithm for solving variational inequality problems in real Hilbert spaces. Under the new assumptions, the cost operator does not need any monotonicity. Moreover, the advantage of the proposed algorithm is that the analysis and proof of its weak convergence use self-adaptive step-sizes without requiring the Lipschitz continuity condition and any line-search rules or adding projection onto the feasible subset. The results of this paper provide new insights into non-monotone variational inequality problems and non-Lipschitz continuity, extending and enriching existing results in the literature. Finally, we give numerical experiments to illustrate the effectiveness of our proposed algorithm.