An explicit iterative algorithm for a class of variational inequalities in Hilbert spaces
Let \(H\) be a Hilbert space and let \(F\) be a strongly monotone Lipschitz-continuous nonlinear operator \(F:H\to{H}\). The problem under consideration is to find a point \(p^\ast\in{C}\) such that \(\langle{F}(p^\ast),\,p=p^\ast\rangle\geq0\) for every \(p\in{C}\). Here, \(C\subset{H}\) is a closed convex set of common fixed points of a finite family of nonexpansive maps \(T_i:H\to{H}\), \(i=1,2,\dots,N\). The authors propose an explicit iterative procedure generating a sequence which strongly converges to the unique solution of the variational inequality.
scientific article; zbMATH DE number 6006018
scientific article