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

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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.

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Acknowledgments

The authors would like to thank the Associate Editor and the anonymous referees for their valuable comments and suggestions which helped us very much in improving the original version of this paper. The work of the second and third authors is supported by VIASM.

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Authors and Affiliations

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

    Dang Van Hieu & Pham Ky Anh

  2. Institute of Mathematics, VAST, Hanoi, 18 Hoang Quoc Viet, Hanoi, Vietnam

    Le Dung Muu

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  1. Dang Van Hieu
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  2. Pham Ky Anh
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  3. Le Dung Muu
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Correspondence to Le Dung Muu.

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Van Hieu, D., Anh, P.K. & Muu, L.D. Modified hybrid projection methods for finding common solutions to variational inequality problems. Comput Optim Appl 66, 75–96 (2017). https://doi.org/10.1007/s10589-016-9857-6

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