Regularization and iterative methods for monotone inverse variational inequalities

@article{Luo2014RegularizationAI,
title={Regularization and iterative methods for monotone inverse variational inequalities},
author={Xue-ping Luo and Jun Yang},
journal={Optimization Letters},
year={2014},
volume={8},
pages={1261-1272}
}

We consider the monotone inverse variational inequality: find $$x\in H$$ such that $$\begin{aligned} f(x)\in \Omega , \quad \left\langle \tilde{f}-f(x),x\right\rangle \ge 0, \quad \forall \tilde{f}\in \Omega , \end{aligned}$$where $$\Omega $$ is a nonempty closed convex subset of a real Hilbert space $$H$$ and $$f:H\rightarrow H$$ is a monotone mapping. A general regularization method for monotone inverse variational inequalities is shown, where the regularizer is a Lipschitz continuous and… Expand