Modulus-based Synchronous Multisplitting Iteration Methods for an Implicit Complementarity Problem

We construct modulus-based synchronous multisplitting iteration methods to solve a large implicit complementarity problem on parallel multiprocessor systems, and prove their convergence. Numerical results confirm our theoretical analysis and show that these new methods are efficient.

On the nonlinear implicit complementarity problem

In this paper, we consider a new class of implicit complementarity problem and study the existence of its solution. An iterative algorithm is also given to find the approximate solution of the new problem and prove that this approximate solution converges to the exact solution. Several special cases are also discussed.

Existence theorems for the implicit complementarity problem

Some existence theorems for the general implicit complementarity problem in an infinite dimensional space are considered.

On the implicit complementarity problem in Hilbert spaces

We consider in this paper the implicit complementarity problem imposed by quasi-variational inequalities and stochastic optimal control. The principal result is an existence theorem for the implicit complementarity problem in Hilbert spaces.