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New Parallel Descent-like Method for Solving a Class of Variational Inequalities

Author

Listed:
  • Z. K. Jiang

    (HuaiHai Institute of Technology)

  • X. M. Yuan

    (Hong Kong Baptist University)

Abstract

To solve a class of variational inequalities with separable structures, some classical methods such as the augmented Lagrangian method and the alternating direction methods require solving two subvariational inequalities at each iteration. The most recent work (B.S. He in Comput. Optim. Appl. 42(2):195–212, 2009) improved these classical methods by allowing the subvariational inequalities arising at each iteration to be solved in parallel, at the price of executing an additional descent step. This paper aims at developing this strategy further by refining the descent directions in the descent steps, while preserving the practical characteristics suitable for parallel computing. Convergence of the new parallel descent-like method is proved under the same mild assumptions on the problem data.

Suggested Citation

  • Z. K. Jiang & X. M. Yuan, 2010. "New Parallel Descent-like Method for Solving a Class of Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 311-323, May.
    • Handle: RePEc:spr:joptap:v:145:y:2010:i:2:d:10.1007_s10957-009-9619-z
    DOI: 10.1007/s10957-009-9619-z
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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. D.R. Han & H.K. Lo, 2002. "New Alternating Direction Method for a Class of Nonlinear Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 112(3), pages 549-560, March.
    3. Bing-Sheng He, 2009. "Parallel splitting augmented Lagrangian methods for monotone structured variational inequalities," Computational Optimization and Applications, Springer, vol. 42(2), pages 195-212, March.
    4. M. H. Xu, 2007. "Proximal Alternating Directions Method for Structured Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 134(1), pages 107-117, July.
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    Cited by:

    1. Wenxing Zhang & Deren Han & Xiaoming Yuan, 2012. "An efficient simultaneous method for the constrained multiple-sets split feasibility problem," Computational Optimization and Applications, Springer, vol. 52(3), pages 825-843, July.
    2. Min Tao & Xiaoming Yuan, 2012. "An inexact parallel splitting augmented Lagrangian method for monotone variational inequalities with separable structures," Computational Optimization and Applications, Springer, vol. 52(2), pages 439-461, June.

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