Journal of Convex Analysis 15 (2008), No. 2, 427--437
Copyright Heldermann Verlag 2008
Well-Posedness of Inverse Variational Inequalities
Dept. of Computational Science, Chengdu University of Information Technology, Chengdu, Sichuan, P. R. China
Dept. of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R. China
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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