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

Zili Wu

European Journal of Operational Research, 2018, vol. 265, issue 2, 448-453

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.

Keywords: Convex programming; Variational inequality; Weak sharpness of solutions; Plus pseudomonotonicity; Gâteaux differentiability of gap functions (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:265:y:2018:i:2:p:448-453

DOI: 10.1016/j.ejor.2017.09.037

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