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Convergence analysis of a modified inexact implicit method for general mixed monotone variational inequalities

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  • Lu-Chuan Zeng
  • Jen-Chih Yao

Abstract

We consider a useful modification of the inexact implicit method with a variable parameter in Wang et al. J Optim Theory 111: 431–443 (2001) for generalized mixed monotone variational inequalities. One of the contributions of the proposed method in this paper is that the restrictions imposed on the variable parameter are weaker than the ones in Wang et al. J Optim Theory 111: 431–443 (2001). Another contribution is that we establish a sufficient and necessary condition for the convergence of the proposed method to a solution of the general mixed monotone variational inequality. Copyright Springer-Verlag Berlin Heidelberg 2005

Suggested Citation

  • Lu-Chuan Zeng & Jen-Chih Yao, 2005. "Convergence analysis of a modified inexact implicit method for general mixed monotone variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(2), pages 211-224, November.
    • Handle: RePEc:spr:mathme:v:62:y:2005:i:2:p:211-224
    DOI: 10.1007/s00186-005-0019-3
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    References listed on IDEAS

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    1. B. S. He & H. Yang & S. L. Wang, 2000. "Alternating Direction Method with Self-Adaptive Penalty Parameters for Monotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 106(2), pages 337-356, August.
    2. S. L. Wang & H. Yang & B. S. He, 2001. "Inexact Implicit Method with Variable Parameter for Mixed Monotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 111(2), pages 431-443, November.
    3. Q. H. Ansari & J. C. Yao, 2001. "Iterative Schemes for Solving Mixed Variational-Like Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 108(3), pages 527-541, March.
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    Cited by:

    1. Pham Ngoc Anh & Qamrul Hasan Ansari & Ho Phi Tu, 2023. "DC auxiliary principle methods for solving lexicographic equilibrium problems," Journal of Global Optimization, Springer, vol. 85(1), pages 129-153, January.

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