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Relaxed projection methods for solving variational inequality problems

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  • Pham Ngoc Anh

    (Posts and Telecommunications Institute of Technology)

Abstract

In this paper, we introduce a new relaxed projection approach for solving the variational inequality problems in a real Hilbert space. First, we propose a solution mapping and show its strongly quasi-nonexpansive properties. Next, we apply the mapping to present two algorithms for solving partially pseudomonotone variational inequality problems and split variational inequality problems. Weak convergence of the algorithms is showed under partially pseudomonotone and Lipschitz continuous assumptions of the cost mappings. Finally, we give some numerical results for the proposed algorithms and comparison with other known methods.

Suggested Citation

  • Pham Ngoc Anh, 2024. "Relaxed projection methods for solving variational inequality problems," Journal of Global Optimization, Springer, vol. 90(4), pages 909-930, December.
    • Handle: RePEc:spr:jglopt:v:90:y:2024:i:4:d:10.1007_s10898-024-01398-w
    DOI: 10.1007/s10898-024-01398-w
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    References listed on IDEAS

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    1. Rapeepan Kraikaew & Satit Saejung, 2014. "Strong Convergence of the Halpern Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 399-412, November.
    2. Yu. Malitsky & V. Semenov, 2015. "A hybrid method without extrapolation step for solving variational inequality problems," Journal of Global Optimization, Springer, vol. 61(1), pages 193-202, January.
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