Well-posedness of inverse variational inequalities

作者：Hu Rong; Fang Ya Ping^*

来源：Journal of Convex Analysis, 2008, 15(2): 427-437.

• inverse variational inequality
• variational inequality
• well-posedness
• metric characterization

Let Omega subset of R(P) be a nonempty closed and convex set and f : R(P) -> R(P) be a function. The inverse variational inequality is to find x* is an element of R(P) such that
f(x*)is an element of Omega, < f'-f(x*),x*>>= 0, for all f' is an element of 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.

• 出版日期2008
• 单位成都信息工程大学; 四川大学