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Modified hybrid projection methods for finding common solutions to variational inequality problems

Author

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  • Dang Hieu

    (Vietnam National University, Hanoi)

  • Pham Ky Anh

    (Vietnam National University, Hanoi)

  • Le Dung Muu

    (VAST, Hanoi)

Abstract

In this paper we propose several modified hybrid projection methods for solving common solutions to variational inequality problems involving monotone and Lipschitz continuous operators. Based on differently constructed half-spaces, the proposed methods reduce the number of projections onto feasible sets as well as the number of values of operators needed to be computed. Strong convergence theorems are established under standard assumptions imposed on the operators. An extension of the proposed algorithm to a system of generalized equilibrium problems is considered and numerical experiments are also presented.

Suggested Citation

  • Dang Hieu & Pham Ky Anh & Le Dung Muu, 2017. "Modified hybrid projection methods for finding common solutions to variational inequality problems," Computational Optimization and Applications, Springer, vol. 66(1), pages 75-96, January.
    • Handle: RePEc:spr:coopap:v:66:y:2017:i:1:d:10.1007_s10589-016-9857-6
    DOI: 10.1007/s10589-016-9857-6
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    References listed on IDEAS

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    1. Y. Censor & A. Gibali & S. Reich, 2011. "The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 318-335, February.
    2. Yu. Malitsky & V. Semenov, 2015. "A hybrid method without extrapolation step for solving variational inequality problems," Journal of Global Optimization, Springer, vol. 61(1), pages 193-202, January.
    3. M. Alizadeh & M. Bianchi & N. Hadjisavvas & R. Pini, 2014. "On cyclic and $$n$$ n -cyclic monotonicity of bifunctions," Journal of Global Optimization, Springer, vol. 60(4), pages 599-616, December.
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    Cited by:

    1. Xiaomei Dong & Xingju Cai & Deren Han & Zhili Ge, 2020. "Solving a Class of Variational Inequality Problems with a New Inexact Strategy," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(01), pages 1-20, January.
    2. Timilehin O. Alakoya & Oluwatosin T. Mewomo & Yekini Shehu, 2022. "Strong convergence results for quasimonotone variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(2), pages 249-279, April.
    3. Dang Hieu & Pham Ky Anh & Le Dung Muu, 2021. "Modified forward–backward splitting method for variational inclusions," 4OR, Springer, vol. 19(1), pages 127-151, March.
    4. Duong Viet Thong & Xiao-Huan Li & Vu Tien Dung & Pham Thi Huong Huyen & Hoang Thi Thanh Tam, 2024. "Using Double Inertial Steps Into the Single Projection Method with Non-monotonic Step Sizes for Solving Pseudomontone Variational Inequalities," Networks and Spatial Economics, Springer, vol. 24(1), pages 1-26, March.
    5. Le Quang Thuy & Trinh Ngoc Hai, 2017. "A Projected Subgradient Algorithm for Bilevel Equilibrium Problems and Applications," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 411-431, November.

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