Projection methods for monotone variational inequalities (Q1305452)

The authors give some new iterative methods for solving monotone variational inequalities of the form \[ \langle Tu,v- u\rangle\geq 0,\;\forall v\in K, \] where \(K\) is a closed convex set in a Hilbert space \(H\), \(T: K\to H\) is a nonlinear operator. The convergence of the given methods requires the monotonicity and pseudomonotonicity of the operator \(T\), whereas the convergence of known methods requires the Lipschitz continuity of the monotone operator \(T\). No numerical tests for the given methods are presented.