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A Novel Method for Finding Minimum-norm Solutions to Pseudomonotone Variational Inequalities

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Abstract

In this paper, we introduce a novel iterative method for finding the minimum-norm solution to a pseudomonotone variational inequality problem in Hilbert spaces. We establish strong convergence of the proposed method and its linear convergence under some suitable assumptions. Some numerical experiments are given to illustrate the performance of our method. Our result improves and extends some existing results in the literature.

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Data Availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The authors are thankful to the handling editor and two anonymous reviewers for comments and remarks which substantially improved the quality of the paper. We also would like to express our gratitude to Professor Terry Friesz, Editor-in-Chief, for giving us the opportunity to revise and resubmit this manuscript.

Funding

The second and the third authors were partially supported by Vietnam Institute for Advanced Study in Mathematics (VIASM).

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Authors and Affiliations

  1. Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, Vietnam

    Duong Viet Thong

  2. Department of Mathematics, University of Science, Vietnam National University, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam

    Pham Ky Anh & Vu Tien Dung

  3. Faculty of Fundamental Science, Hanoi University of Industry, 298 Cau Dien Street, Bac Tu Liem District, Hanoi, Vietnam

    Do Thi My Linh

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  1. Duong Viet Thong
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  2. Pham Ky Anh
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  3. Vu Tien Dung
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  4. Do Thi My Linh
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Correspondence to Vu Tien Dung.

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Thong, D.V., Anh, P.K., Dung, V.T. et al. A Novel Method for Finding Minimum-norm Solutions to Pseudomonotone Variational Inequalities. Netw Spat Econ 23, 39–64 (2023). https://doi.org/10.1007/s11067-022-09569-6

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