ASYNCHRONOUS PARALLEL NONLINEAR MULTISPLITTING RELAXATION METHODS FORLARGE SPARSE NONLINEAR COMPLEMENTARITY-PROBLEMS

In accordance with the principle of sufficiently using delayed informa tion, and making use of the nonlinear multisplitting and the nonlinear relaxation techniques, we present in this paper a class of asynchrono us parallel nonlinear multisplitting successive overrelaxation (SOR) m ethods 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-St effensen method. Under suitable conditions we establish the local conv ergence theory of this class of new methods. Numerical imitations show that our new methods are feasible and efficient for solving the nonli near complementarity problems on the MIMD multiprocessor systems. (C) 1998 Elsevier Science Inc. All rights reserved.