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A new iterative method for solving pseudomonotone variational inequalities with non-Lipschitz operators

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Abstract

The purpose of this paper is to study and analyze a new projection-type algorithm for solving pseudomonotone variational inequality problems in real Hilbert spaces. The advantage of the proposed algorithm is the strong convergence proved without assuming Lipschitz continuity of the associated mapping. In addition, the proposed algorithm uses only two projections onto the feasible set in each iteration. The numerical behaviors of the proposed algorithm on a test problem are illustrated and compared with several previously known algorithms.

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Acknowledgements

The authors would like to thank Associate Editor and 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.

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Authors and Affiliations

  1. Institute of Research and Development, Duy Tan University, Da Nang, 550000, Vietnam

    Duong Viet Thong

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

    Yekini Shehu

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

    Olaniyi S. Iyiola

Authors
  1. Duong Viet Thong
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  2. Yekini Shehu
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  3. Olaniyi S. Iyiola
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Correspondence to Duong Viet Thong.

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Communicated by Paulo J. S. Silva.

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Thong, D.V., Shehu, Y. & Iyiola, O.S. A new iterative method for solving pseudomonotone variational inequalities with non-Lipschitz operators. Comp. Appl. Math. 39, 108 (2020). https://doi.org/10.1007/s40314-020-1136-6

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  • DOI: https://doi.org/10.1007/s40314-020-1136-6

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