关键词: 逆变分不等式, 强单调, 不动点, 迭代算法

Abstract:

Let C be a nonempty closed convex subset of a real Hilbert space H, f:H→H be a Lipschitz continuous and strongly monotone mapping. Then, inverse variational inequality is considered (in short, IVI (C, f));find ξ∈H such that f(ξ)∈C,＜ξ,v - f(ξ)＞≥0,∀v∈C.A new existence and uniqueness theorem for inverse variational inequalities is proved and two iterative algorithms are introduced to improve the previous relevant results.

Key words: inverse variational inequality, strongly monotone, fixed point, iterative algorithm