Splitting Algorithm for Solving Mixed Variational Inequalities with Inversely Strongly Monotone Operators

摘要

We consider a boundary value problem whose generalized statement is formulated as a mixed variational inequality in a Hilbert space. The operator of this variational inequality is a sum of several in-versely strongly monotone operators (which are not necessarily potential operators). The functional occurring in this variational inequality is also a sum of several lower semi-continuous convex proper functionals. For solving of the considered variational inequality a decomposition iterative method is offered. The suggested method does not require the inversion of original operators. The convergence of this method is investigated.