Regularized dynamics for monotone inverse variational inequalities in hilbert spaces

Abstract

In this paper, we present a regularized dynamical system method for solving monotone inverse variational inequalities (IVIs) in infinite dimensional Hilbert spaces. It is shown that the corresponding Cauchy problem admits a unique strong global solution, whose limit at infinity exists and solves the given monotone IVI. Then by discretizing the dynamical system, we obtain a class of iterative regularization algorithms with relaxation parameters, which are strongly convergent under quite mild assumptions on the cost operator. Some simple numerical examples, including an infinite dimensional one, are given to illustrate the performance of the proposed algorithms.