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A hybrid extragradient method for general variational inequalities

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  • L. Zeng
  • J. Yao

Abstract

In this paper, we introduce and study a hybrid extragradient method for finding solutions of a general variational inequality problem with inverse-strongly monotone mapping in a real Hilbert space. An iterative algorithm is proposed by virtue of the hybrid extragradient method. Under two sets of quite mild conditions, we prove the strong convergence of this iterative algorithm to the unique common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the general variational inequality problem, respectively. Copyright Springer-Verlag 2009

Suggested Citation

  • L. Zeng & J. Yao, 2009. "A hybrid extragradient method for general variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 141-158, March.
    • Handle: RePEc:spr:mathme:v:69:y:2009:i:1:p:141-158
    DOI: 10.1007/s00186-008-0215-z
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    References listed on IDEAS

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    1. L. C. Zeng & S. Schaible & J. C. Yao, 2005. "Iterative Algorithm for Generalized Set-Valued Strongly Nonlinear Mixed Variational-Like Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 124(3), pages 725-738, March.
    2. W. Takahashi & M. Toyoda, 2003. "Weak Convergence Theorems for Nonexpansive Mappings and Monotone Mappings," Journal of Optimization Theory and Applications, Springer, vol. 118(2), pages 417-428, August.
    3. N. Nadezhkina & W. Takahashi, 2006. "Weak Convergence Theorem by an Extragradient Method for Nonexpansive Mappings and Monotone Mappings," Journal of Optimization Theory and Applications, Springer, vol. 128(1), pages 191-201, January.
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