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Super Efficiency of Multicriterion Network Equilibrium Model and Vector Variational Inequality

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Listed:
  • Yunan Wu

    (Beijing Foreign Studies University)

  • Yuchen Peng

    (Renmin University of China)

  • Long Peng

    (Beijing Foreign Studies University)

  • Ling Xu

    (Beijing Foreign Studies University)

Abstract

The super efficiency of a vector variational inequality is considered in this paper. We show that for both the single and multiple criteria cases, a network equilibrium model can be recast as super efficient solutions to a kind of variational inequality. For the network equilibrium model with a vector-valued cost function, we derive the necessary and sufficient condition in terms of the super efficiency of a vector variational inequality by using the Gerstewitz’s function without any convex assumptions.

Suggested Citation

  • Yunan Wu & Yuchen Peng & Long Peng & Ling Xu, 2012. "Super Efficiency of Multicriterion Network Equilibrium Model and Vector Variational Inequality," Journal of Optimization Theory and Applications, Springer, vol. 153(2), pages 485-496, May.
    • Handle: RePEc:spr:joptap:v:153:y:2012:i:2:d:10.1007_s10957-011-9950-z
    DOI: 10.1007/s10957-011-9950-z
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    References listed on IDEAS

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    1. G. Y. Chen & C. J. Goh & X. Q. Yang, 1999. "Vector network equilibrium problems and nonlinear scalarization methods," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(2), pages 239-253, April.
    2. X. Q. Yang & C. J. Goh, 1997. "On Vector Variational Inequalities: Application to Vector Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 95(2), pages 431-443, November.
    3. Li, S.J. & Teo, K.L. & Yang, X.Q., 2008. "A remark on a standard and linear vector network equilibrium problem with capacity constraints," European Journal of Operational Research, Elsevier, vol. 184(1), pages 13-23, January.
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