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A New Decomposition Method for Variational Inequalities with Linear Constraints

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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.

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Authors and Affiliations

  1. School of Mathematical Sciences and Key Laboratory for NSLSCS of Jiangsu Province, Nanjing Normal University, Nanjing, 210046, P.R. China

    Min Zhang & Deren Han

  2. School of Computer Science, Nanjing Normal University, Nanjing, 210097, P.R. China

    Gang Qian

  3. Department of Mathematics, Taiyuan Normal University, Taiyuan, Shanxi, 030012, China

    Xihong Yan

Authors
  1. Min Zhang
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  2. Deren Han
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  3. Gang Qian
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  4. Xihong Yan
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Corresponding author

Correspondence to Deren Han.

Additional information

Communicated by Nicolas Hadjisavvas.

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Zhang, M., Han, D., Qian, G. et al. A New Decomposition Method for Variational Inequalities with Linear Constraints. J Optim Theory Appl 152, 675–695 (2012). https://doi.org/10.1007/s10957-011-9931-2

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  • DOI: https://doi.org/10.1007/s10957-011-9931-2

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