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Generalized Differential Properties of the Auslender Gap Function for Variational Inequalities

Author

Listed:
  • S. J. Li

    (Chongqing University)

  • S. H. Hou

    (Hong Kong Polytechnic University)

  • G. Y. Chen

    (Chinese Academy of Science)

Abstract

In this note, the Auslender gap function, which is used to formulate a variational inequality into an equivalent minimization problem, is shown to be differentiable in the generalized sense and has a lower contingent derivative under suitable conditions. This enables us to establish necessary and sufficient conditions for the existence of a solution to problems of variational inequalities.

Suggested Citation

  • S. J. Li & S. H. Hou & G. Y. Chen, 2005. "Generalized Differential Properties of the Auslender Gap Function for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 124(3), pages 739-749, March.
    • Handle: RePEc:spr:joptap:v:124:y:2005:i:3:d:10.1007_s10957-004-1183-y
    DOI: 10.1007/s10957-004-1183-y
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    References listed on IDEAS

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    1. Stella Dafermos, 1988. "Sensitivity Analysis in Variational Inequalities," Mathematics of Operations Research, INFORMS, vol. 13(3), pages 421-434, August.
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