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Weak sharp minima for set-valued vector variational inequalities with an application

Author

Listed:
  • Li, J.
  • Huang, N.J.
  • Yang, X.Q.

Abstract

In this paper, the notion of weak sharp minima is employed to the investigation of set-valued vector variational inequalities. The gap function [phi]T for set-valued strong vector variational inequalities (for short, SVVI) is proved to be less than the gap function [phi]T for set-valued weak vector variational inequalities (for short, WVVI) under certain conditions, which implies that the solution set of SVVI is equivalent to the solution set of WVVI. Moreover, it is shown that weak sharp minima for the solution sets of SVVI and WVVI hold for and for gap functions and under the assumption of strong pseudomonotonicity, where pTi is a gap function for i-th component of SVVI and WVVI. As an application, the weak Pareto solution set of vector optimization problems (for short, VOP) is proved to be weak sharp minimum for when each component gi of objective function is strongly convex.

Suggested Citation

  • Li, J. & Huang, N.J. & Yang, X.Q., 2010. "Weak sharp minima for set-valued vector variational inequalities with an application," European Journal of Operational Research, Elsevier, vol. 205(2), pages 262-272, September.
    • Handle: RePEc:eee:ejores:v:205:y:2010:i:2:p:262-272
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    References listed on IDEAS

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    1. X.Q. Yang & J.C. Yao, 2002. "Gap Functions and Existence of Solutions to Set-Valued Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 115(2), pages 407-417, November.
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    Cited by:

    1. Wu, Zili, 2018. "Characterizations of weakly sharp solutions for a variational inequality with a pseudomonotone mapping," European Journal of Operational Research, Elsevier, vol. 265(2), pages 448-453.
    2. Shipra Singh & Savin Treanţă, 2021. "Characterization results of weak sharp solutions for split variational inequalities with application to traffic analysis," Annals of Operations Research, Springer, vol. 302(1), pages 265-287, July.

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