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A note on vector network equilibrium principles

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Abstract

An example is given to show that the necessary conditions of Theorem 4.5 [in Chen et al. Math Methods Oper Res 49:239–253, 1999] and Theorem 2.1 (i) [in Goh and Yang Eur J Oper Res 116:615–628, 1999] for (weak) vector equilibrium flows may not hold. New ξ-equilibrium and parametric equilibrium flows are introduced. As a result, necessary and sufficient conditions between a weak vector equilibrium flow and an ξ-equilibrium flow and between a vector equilibrium flow and a parametric equilibrium flow are established.

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References

  • Chen GY, Yen ND (1993) On the variational inequality model for network equilibrium. Internal Report 3.196 (724), Department of Mathematics, University of Pisa

  • Chen GY, Goh CJ, Yang XQ (1999) Vector network equilibrium problems and nonlinear scalarization methods. Math Methods Oper Res 49:239–253

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  • Goh CJ, Yang XQ (1999) Vector equilibrium problem and vector optimization. Eur J Oper Res 116:615–628

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Authors and Affiliations

  1. College of Mathematics and Science, Chongqing University, Chongqing, 400044, China

    S. J. Li

  2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China

    X. Q. Yang

  3. Institute of Systems Science, Chinese Academy of Science, Beijing, 100080, China

    G. Y. Chen

Authors
  1. S. J. Li
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  2. X. Q. Yang
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  3. G. Y. Chen
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Correspondence to S. J. Li.

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Li, S.J., Yang, X.Q. & Chen, G.Y. A note on vector network equilibrium principles. Math Meth Oper Res 64, 327–334 (2006). https://doi.org/10.1007/s00186-006-0089-x

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  • DOI: https://doi.org/10.1007/s00186-006-0089-x

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