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An Inexact Alternating Direction Method for Structured Variational Inequalities

Author

Listed:
  • Zhongming Chen

    (Nankai University)

  • Li Wan

    (Nankai University)

  • Qingzhi Yang

    (Nankai University)

Abstract

Recently, the alternating direction method of multipliers has attracted great attention. For a class of variational inequalities (VIs), this method is efficient, when the subproblems can be solved exactly. However, the subproblems could be too difficult or impossible to be solved exactly in many practical applications. In this paper, we propose an inexact method for structured VIs based on the projection and contraction method. Instead of solving the subproblems exactly, we use the simple projection to get a predictor and correct it to approximate the subproblems’ real solutions. The convergence of the proposed method is proved under mild assumptions and its efficiency is also verified by some numerical experiments.

Suggested Citation

  • Zhongming Chen & Li Wan & Qingzhi Yang, 2014. "An Inexact Alternating Direction Method for Structured Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 439-459, November.
    • Handle: RePEc:spr:joptap:v:163:y:2014:i:2:d:10.1007_s10957-014-0522-x
    DOI: 10.1007/s10957-014-0522-x
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    References listed on IDEAS

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    1. 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.
    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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