A Class of Projection and Contraction Methods for Monotone Variational Inequalities

摘要

In this paper we introduce a new class of iterative methods for solving the monotone variational inequalities u~*∈Ω, (u-u~*)~T F(u~*) ≥0, A u ∈Ω. Each iteration of the methods presented consists essentially only of the computation of F(u), a projection to Ω, v:=P_Ω[u-F(u)] , and the mapping F(v). The distance of the iterates to the solution set monotonically converges to zero. Both the methods and the convergence proof are quite simple.