Some iterative methods for nonconvex variational inequalities (Q1956455)

For a given nonlinear operator \(T\), the problem of finding \(u\in K\), \(\langle Tu, v- u\rangle\geq 0\), \(\forall v\in K_r\) is called the nonconvex variational inequality. This problem is equivalentto finding \(u\in K\), such that \(0\in Tu+ N^P_{K_r}(u)\). Using this equivalent alternative formulation, a new class of two-step iterative methods is discussed. Furthermore, a new class of Wiener-Hopf equations is introduced and the equivalence between this class and the nonconvex variational inequalities is established and some iterative methods are proposed.