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Inexact Implicit Method with Variable Parameter for Mixed Monotone Variational Inequalities

Author

Listed:
  • S. L. Wang

    (Nanjing University)

  • H. Yang

    (Hong Kong University of Science and Technology)

  • B. S. He

    (Nanjing University)

Abstract

In this paper, we focus on a useful modification of the implicit method by Noor (Ref. 1) for mixed variational inequalities. Experience on applications has shown that the number of iterations of the original method depends significantly on the penalty parameter. One of the contributions of the proposed method is that we allow the penalty parameter to be variable. By introducing a self-adaptive rule, we find that our method is more flexible and efficient than the original one. Another contribution is that we require only an inexact solution of the nonlinear equations at each iteration. A detailed convergence analysis of our method is also included.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:111:y:2001:i:2:d:10.1023_a:1011942620208
    DOI: 10.1023/A:1011942620208
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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.
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    Cited by:

    1. Sarah Perrin & Thierry Roncalli, 2019. "Machine Learning Optimization Algorithms & Portfolio Allocation," Papers 1909.10233, arXiv.org.
    2. 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.

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