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Differential and sensitivity properties of gap functions for vector variational inequalities

Author

Listed:
  • S. J. Li
  • Hong Yan
  • G. Y. Chen

Abstract

The purpose of this paper is to investigate differential properties of a class of set-valued maps and gap functions involving vector variational inequalities. Relationship between their contingent derivatives are discussed. A formula computing contingent derivative of the gap functions is established. Optimality conditions of solutions for vector variational inequalities are obtained. Copyright Springer-Verlag Berlin Heidelberg 2003

Suggested Citation

  • S. J. Li & Hong Yan & G. Y. Chen, 2003. "Differential and sensitivity properties of gap functions for vector variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(3), pages 377-391, August.
    • Handle: RePEc:spr:mathme:v:57:y:2003:i:3:p:377-391
    DOI: 10.1007/s001860200254
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    Cited by:

    1. S. Li & M. Li, 2009. "Levitin–Polyak well-posedness of vector equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 125-140, March.
    2. M. H. Li & S. J. Li, 2010. "Second-Order Differential and Sensitivity Properties of Weak Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 144(1), pages 76-87, January.
    3. Xiang-Kai Sun & Sheng-Jie Li, 2014. "Generalized second-order contingent epiderivatives in parametric vector optimization problems," Journal of Global Optimization, Springer, vol. 58(2), pages 351-363, February.
    4. Yong Zhao & Jin Zhang & Xinmin Yang & Gui-Hua Lin, 2017. "Expected Residual Minimization Formulation for a Class of Stochastic Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 545-566, November.

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