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Using Double Inertial Steps Into the Single Projection Method with Non-monotonic Step Sizes for Solving Pseudomontone Variational Inequalities

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Abstract

In this paper, we propose a new modified algorithm for finding an element of the set of solutions of a pseudomonotone, Lipschitz continuous variational inequality problem in real Hilbert spaces. Using the technique of double inertial steps into a single projection method we give weak and strong convergence theorems of the proposed algorithm. The weak convergence does not require prior knowledge of the Lipschitz constant of the variational inequality mapping and only computes one projection onto a feasible set per iteration as well as without using the sequentially weak continuity of the associated mapping. Under additional strong pseudomonotonicity and Lipschitz continuity assumptions, the R-linear convergence rate of the proposed algorithm is presented. Finally, some numerical examples are given to illustrate the effectiveness of the algorithms.

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Data Availability

The datasets generated during and/or analyzed 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. The authors would like to thank Professor Pham Ky Anh for drawing our attention to the subject and for many useful discussions. This research has been done under the research project QG.23.04 of Vietnam National University, Hanoi.

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Authors and Affiliations

  1. Faculty of Economics Mathematics, National Economics University, Hanoi City, Vietnam

    Duong Viet Thong, Pham Thi Huong Huyen & Hoang Thi Thanh Tam

  2. School of Mathematics and Statistics, Shandong University of Technology, Zibo, 255000, China

    Xiao-Huan Li

  3. University of Science, Vietnam National University, Hanoi, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam

    Vu Tien Dung

Authors
  1. Duong Viet Thong
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  2. Xiao-Huan Li
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  3. Vu Tien Dung
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  4. Pham Thi Huong Huyen
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  5. Hoang Thi Thanh Tam
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Contributions

D. V. Thong, P. T. H. Huyen and H. T. T. Tam wrote the main manuscript text and Xiao-Huan Li and V. T. Dung prepared Figs. 1–8. All authors reviewed the manuscript carefully.

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Correspondence to Vu Tien Dung.

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Thong, D.V., Li, XH., Dung, V.T. et al. Using Double Inertial Steps Into the Single Projection Method with Non-monotonic Step Sizes for Solving Pseudomontone Variational Inequalities. Netw Spat Econ 24, 1–26 (2024). https://doi.org/10.1007/s11067-023-09606-y

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