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A Novel Inertial Projection and Contraction Method for Solving Pseudomonotone Variational Inequality Problems

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Abstract

In this paper, we introduce a new algorithm which combines the inertial contraction projection method and the Mann-type method (Mann in Proc. Am. Math. Soc. 4:506–510, 1953) for solving monotone variational inequality problems in real Hilbert spaces. The strong convergence of our proposed algorithm is proved under some standard assumptions imposed on cost operators. Finally, we give some numerical experiments to illustrate the proposed algorithm and the main result.

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Acknowledgements

The authors would like to thank three anonymous reviewers for their comments on the manuscript which helped us very much in improving and presenting the original version of this paper. This work is supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under the project: 101.01-2019.320. P. Cholamjiak was supported by Thailand Research Fund and University of Phayao under the project RSA6180084 and UOE62001. This work was partially supported by Thailand Science Research and Innovation under the project IRN62W0007.

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Authors and Affiliations

  1. School of Science, University of Phayao, Phayao, 56000, Thailand

    Prasit Cholamjiak

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

    Duong Viet Thong

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

    Yeol Je Cho

  4. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, P.R. China

    Yeol Je Cho

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  1. Prasit Cholamjiak
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  2. Duong Viet Thong
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  3. Yeol Je Cho
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Correspondence to Duong Viet Thong.

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Dedicated to Professor Pham Ky Anh on the occasion of his 70th birthday

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Cholamjiak, P., Thong, D.V. & Cho, Y.J. A Novel Inertial Projection and Contraction Method for Solving Pseudomonotone Variational Inequality Problems. Acta Appl Math 169, 217–245 (2020). https://doi.org/10.1007/s10440-019-00297-7

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