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Characterizations of weakly sharp solutions for a variational inequality with a pseudomonotone mapping

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  • Wu, Zili

Abstract

For a variational inequality problem with a pseudomonotone mapping F, we characterize the weak sharpness of its solution set C* without using gap functions. When the mapping F is also constant on C*, the characterizations of weak sharpness of C* become more succinct. As an example, a pseudomonotone+ mapping on C* is shown to be constant on C*. Consequently the weak sharpness of C* can further be described by a Gâteaux differentiable function which itself characterizes the pseudomonotonicity+ of F on C*. It turns out that several existing relevant results with differentiable gap functions can be obtained from ours.

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  • 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.
    • Handle: RePEc:eee:ejores:v:265:y:2018:i:2:p:448-453
    DOI: 10.1016/j.ejor.2017.09.037
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    Cited by:

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    2. Luong Nguyen & Qamrul Hasan Ansari & Xiaolong Qin, 2020. "Linear conditioning, weak sharpness and finite convergence for equilibrium problems," Journal of Global Optimization, Springer, vol. 77(2), pages 405-424, June.
    3. Ruyu Wang & Wenling Zhao & Daojin Song & Yaozhong Hu, 2024. "The Augmented Weak Sharpness of Solution Sets in Equilibrium Problems," Mathematics, MDPI, vol. 12(2), pages 1-23, January.

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