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New strong convergence theorem of the inertial projection and contraction method for variational inequality problems

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Abstract

In this paper, we introduce a new algorithm which combines the inertial projection and contraction method and the viscosity method for solving monotone variational inequality problems in real Hilbert spaces and prove a strong convergence theorem of our proposed algorithm under the standard assumptions imposed on cost operators. Finally, we give some numerical experiments to illustrate the proposed algorithm.

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Acknowledgments

The authors would like to thank Professor Aviv Gibali and two anonymous reviewers for their comments on the manuscript which helped us very much in improving and presenting the original version of this paper.

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Authors and Affiliations

  1. Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Duong Viet Thong

  2. Department of Mathematics, University of Transport and Communications, 3 Cau Giay Street, Hanoi, Vietnam

    Nguyen The Vinh

  3. Department of Mathematics Education and the RINS, Gyeongsang National University, Jinju, 52828, Korea

    Yeol Je Cho

  4. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, Sichuan, People’s Republic of China

    Yeol Je Cho

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  1. Duong Viet Thong
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Correspondence to Duong Viet Thong.

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Thong, D.V., Vinh, N.T. & Cho, Y.J. New strong convergence theorem of the inertial projection and contraction method for variational inequality problems. Numer Algor 84, 285–305 (2020). https://doi.org/10.1007/s11075-019-00755-1

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