Journal of Convex Analysis 15 (2008), No. 2, 427--437
Copyright Heldermann Verlag 2008
Well-Posedness of Inverse Variational Inequalities
Rong Hu
Dept. of Computational Science, Chengdu University of Information Technology, Chengdu, Sichuan, P. R. China
Ya-Ping Fang
Dept. of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R. China
fabhcn@yahoo.com.cn
[Abstract-pdf]
Let $\Omega\subset R^P$ be a nonempty closed and convex set and $f:R^P\to R^P$ be a function. The inverse variational inequality is to find $x^*\in R^P$ such that $$ f(x^*)\in \Omega,\quad \langle f'-f(x^*),x^*\rangle\ge 0,\quad \forall f'\in \Omega. $$ The purpose of this paper is to investigate the well-posedness of the inverse variational inequality. We establish some characterizations of its well-posedness. We prove that under suitable conditions, the well-posedness of an inverse variational inequality is equivalent to the existence and uniqueness of its solution. Finally, we show that the well-posedness of an inverse variational inequality is equivalent to the well-posedness of an enlarged classical variational inequality.
Keywords: Inverse variational inequality, variational inequality, well-posedness, metric characterization.
MSC: 49J40, 49K40
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