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A New Decomposition Method for Variational Inequalities with Linear Constraints

Author

Listed:
  • Min Zhang

    (Nanjing Normal University)

  • Deren Han

    (Nanjing Normal University)

  • Gang Qian

    (Nanjing Normal University)

  • Xihong Yan

    (Taiyuan Normal University)

Abstract

We propose a new decomposition method for solving a class of monotone variational inequalities with linear constraints. The proposed method needs only to solve a well-conditioned system of nonlinear equations, which is much easier than a variational inequality, the subproblem in the classic alternating direction methods. To make the method more flexible and practical, we solve the sub-problems approximately. We adopt a self-adaptive rule to adjust the parameter, which can improve the numerical performance of the algorithm. Under mild conditions, the underlying mapping be monotone and the solution set of the problem be nonempty, we prove the global convergence of the proposed algorithm. Finally, we report some preliminary computational results, which demonstrate the promising performance of the new algorithm.

Suggested Citation

  • Min Zhang & Deren Han & Gang Qian & Xihong Yan, 2012. "A New Decomposition Method for Variational Inequalities with Linear Constraints," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 675-695, March.
    • Handle: RePEc:spr:joptap:v:152:y:2012:i:3:d:10.1007_s10957-011-9931-2
    DOI: 10.1007/s10957-011-9931-2
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    References listed on IDEAS

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    1. D. Han, 2007. "Inexact Operator Splitting Methods with Selfadaptive Strategy for Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 132(2), pages 227-243, February.
    2. B. S. He & H. Yang & Q. Meng & D. R. Han, 2002. "Modified Goldstein–Levitin–Polyak Projection Method for Asymmetric Strongly Monotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 112(1), pages 129-143, January.
    3. Anna Nagurney & Padma Ramanujam, 1996. "Transportation Network Policy Modeling with Goal Targets and Generalized Penalty Functions," Transportation Science, INFORMS, vol. 30(1), pages 3-13, February.
    4. 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.
    5. B. S. He & L. Z. Liao, 2002. "Improvements of Some Projection Methods for Monotone Nonlinear Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 112(1), pages 111-128, January.
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