Applications of fixed-point methods to discrete variational and quasi- variational inequalities
Discrete analogues of variational inequalities (VI) and quasi-variational inequalities (QVI), encountered in stochastic control and mathematical physics, are discussed. It is shown that those discrete VI's and QVI's can be written in the fixed point form \(x=Tx\) such that either T or some power of T is a contraction. This leads to globally convergent iterative methods for the solution of discret VI's and QVI's, which are very suitable for implementation on parallel computers with single- instruction, multiple-data architecture, particularly on massive parallel processors.
scientific article; zbMATH DE number 3992829
scientific article