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Novel projection methods for solving variational inequality problems and applications

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Abstract

We introduce and analyze two modified subgradient extragradient methods with adaptive step sizes for solving variational inequality problems governed by pseudomonotone and Lipschitz continuous operators in real Hilbert spaces. For the first algorithm, a sufficient condition for weak convergence is established under pseudomonotonicity and Lipschitz continuity assumptions, with a possibly unknown Lipschitz constant. A sufficient condition for weak convergence for the second algorithm is proved under pseudomonotonicity and uniform continuity assumptions. We also establish an R-linear rate of convergence under strong pseudomonotonicity and Lipschitz continuity hypotheses regarding the variational inequality operator. Finally, we present several numerical computational experiments which involve a comparison of our proposed algorithms with other algorithms in some real-life applications.

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Authors and Affiliations

  1. Division of Applied Mathematics, Thu Dau Mot University, Thu Dau Mot, Binh Duong Province, Vietnam

    Duong Viet Thong

  2. Department of Mathematics, The Technion – Israel Institute of Technology, 32000, Haifa, Israel

    Simeon Reich

  3. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, People’s Republic of China

    Yekini Shehu

  4. Department of Mathematics, Computer Science and Information Systems, California University of Pennsylvania, Pennsylvania, PA, USA

    Olaniyi S. Iyiola

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  1. Duong Viet Thong
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  2. Simeon Reich
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  3. Yekini Shehu
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  4. Olaniyi S. Iyiola
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Correspondence to Duong Viet Thong or Simeon Reich.

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Thong, D.V., Reich, S., Shehu, Y. et al. Novel projection methods for solving variational inequality problems and applications. Numer Algor 93, 1105–1135 (2023). https://doi.org/10.1007/s11075-022-01457-x

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