
Journal of Convex Analysis 15 (2008), No. 2, 427437 Copyright Heldermann Verlag 2008 WellPosedness of Inverse Variational Inequalities Rong Hu Dept. of Computational Science, Chengdu University of Information Technology, Chengdu, Sichuan, P. R. China YaPing Fang Dept. of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R. China fabhcn@yahoo.com.cn [Abstractpdf] 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 wellposedness of the inverse variational inequality. We establish some characterizations of its wellposedness. We prove that under suitable conditions, the wellposedness of an inverse variational inequality is equivalent to the existence and uniqueness of its solution. Finally, we show that the wellposedness of an inverse variational inequality is equivalent to the wellposedness of an enlarged classical variational inequality. Keywords: Inverse variational inequality, variational inequality, wellposedness, metric characterization. MSC: 49J40, 49K40 [ Fulltextpdf (120 KB)] for subscribers only. 