Applications of fixed-point methods to discrete variational and quasi-variational inequalities

Summary In this paper, discrete analogues of variational inequalities (V.I.) and quasi-variational inequalities (Q.V.I.), encountered in stochastic control and mathematical physics, are discussed.It is shown that those discrete V.I.'s and Q.V.I.'s can be written in the fixed point formx=Tx such that eitherT or some power ofT is a contraction. This leads to globally convergent iterative methods for the solution of discrete V.I.'s and Q.V.I.'s, which are very suitable for implementation on parallel computers with single-instruction, multiple-data architecture, particularly on massively parallel processors (M.P.P.'s).This research is in part supported by the U.S. Department of Energy, Engineering Research Program, under Contract No. DE-AS05-84EH13145