Fast modulus-based matrix splitting iteration methods for implicit complementarity problems

Abstract

Implicit complementarity problems (ICPs) have attracted a great deal of attention in recent years. To this end, fast modulus-based matrix splitting iteration methods for ICPs are studied in this paper. We first reformulate the ICP as a fixed-point equation. Then we propose our fast methods and prove the convergence under some assumptions. By suitably adopting the relations between the solutions of the ICP and the equivalent one, computation cost of the proposed methods is reduced compared with some existing methods. This advantage is verified by numerical experiments, which illustrate that our methods are much more practical in applications.