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A New Implementable Prediction‐Correction Method for Monotone Variational Inequalities with Separable Structure

Author

Listed:
  • Feng Ma
  • Mingfang Ni
  • Zhanke Yu

Abstract

The monotone variational inequalities capture various concrete applications arising in many areas. In this paper, we develop a new prediction‐correction method for monotone variational inequalities with separable structure. The new method can be easily implementable, and the main computational effort in each iteration of the method is to evaluate the proximal mappings of the involved operators. At each iteration, the algorithm also allows the involved subvariational inequalities to be solved in parallel. We establish the global convergence of the proposed method. Preliminary numerical results show that the new method can be competitive with Chen′s proximal‐based decomposition method in Chen and Teboulle (1994).

Suggested Citation

  • Feng Ma & Mingfang Ni & Zhanke Yu, 2013. "A New Implementable Prediction‐Correction Method for Monotone Variational Inequalities with Separable Structure," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:941861
    DOI: 10.1155/2013/941861
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    References listed on IDEAS

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    1. Stella Dafermos, 1980. "Traffic Equilibrium and Variational Inequalities," Transportation Science, INFORMS, vol. 14(1), pages 42-54, February.
    2. R. T. Rockafellar, 1976. "Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 97-116, May.
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