Iterative algorithms for semi-linear quasi complementarity problems

AbstractIn this paper, we consider an iterative for a class of quasi complementarity problems of finding u ϵ Rn such that g(u) ϵ K(u), (Mu + q) ϵ K∗(u), (g(u), Mu + q) = 0, where g is a continuous mapping from Rn into itself, M ϵ Rn x n, q ϵ Rn, and K∗(u) is the polar cone of the convex cone K(u) in Rn. The algorithms considered in this paper are general and unifying ones, which include many existing algorithms as special cases for solving the complementarity problems. We also study the convergence criteria of the general algorithms