AN EXTENDED GAUSS-SEIDEL METHOD FOR A CLASS OF MULTI-VALUED COMPLEMENTARITY PROBLEMS

The complementarity problem is one of the basic topics in nonlinear analysis; however, the methods for solving complementarity problems are usually developed for problems with single-valued mappings. In this paper we examine a class of complementarity problems with multi-valued mappings and propose an extension of the Gauss–Seidel algorithm for finding its solution. Its convergence is proved under off-diagonal antitonicity assumptions. Applications to Walrasian type equilibrium problems and to nonlinear input–output problems are also given.