A hybrid projection-proximal point algorithm is proposed for variational inequality problems. Though the usual proximal point method and its variants require that the mapping involved be monotone, at least pseudomonotone, we assume only that the so-called Minty variational inequality has a solution, in order to ensure the global convergence. This assumption is less stringent than pseudomonotonicity. In particular, it applies to quasimonotone variational inequality having a nontrivial solution.
View A hybrid projection-proximal point algorithm for solving nonmonotone variational inequality problems