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Self adaptive inertial subgradient extragradient algorithms for solving pseudomonotone variational inequality problems

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Abstract

In this paper, two new algorithms are introduced for solving a pseudomontone variational inequality problem with a Lipschitz condition in a Hilbert space. The algorithms are constructed around three methods: the subgradient extragradient method, the inertial method and the viscosity method. With a new stepsize rule is incorporated, the algorithms work without any information of Lipschitz constant of operator. The weak convergence of the first algorithm is established, while the second one is strongly convergent which comes from the viscosity method. In order to show the computational effectiveness of our algorithms, some numerical results are provided.

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Acknowledgements

The authors would like to thank anonymous reviewrs 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.

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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, College of Air Force, Nha Trang, Vietnam

    Dang Van Hieu

  3. Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780, Athens, Greece

    Themistocles M. Rassias

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  1. Duong Viet Thong
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  2. Dang Van Hieu
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  3. Themistocles M. Rassias
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Correspondence to Duong Viet Thong.

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This paper is dedicated to Professor Pham Ky Anh on the occasion of his 70th birthday.

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Thong, D.V., Van Hieu, D. & Rassias, T.M. Self adaptive inertial subgradient extragradient algorithms for solving pseudomonotone variational inequality problems. Optim Lett 14, 115–144 (2020). https://doi.org/10.1007/s11590-019-01511-z

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