Asynchronous parallel nonlinear multisplitting relaxation methods for large sparse nonlinear complementarity problems

摘要

In accordance with the principle of sufficiently using delayed information, and making use of the nonlinear multisplitting and the nonlinear relaxation techniques, we present in this paper a class of asynchronous parallel nonlinear multisplitting successive overrelaxation (SOR) methods for solving large sparse nonlinear complementarity problems on high-speed MIMD multiprocessor systems. These new methods particularly include the so-called asynchronous parallel nonlinear multisplitting SOR-Newton method, asynchronous parallel nonlinear multisplitting SOR-chord method and asynchronous parallel nonlinear multisplitting SOR-Steffensen method. Under suitable conditions we establish the local convergence theory of this class of new methods. Numerical imitations show that our new methods are feasible and efficient for solving the nonlinear complementarity problems on the MIMD multiprocessor systems.