An exact penalty method for monotone variational inequalities and order optimal algorithms for finding saddle points (Q647888)

The author considers variational inequalities in a Banach space of the following form \[ x\in Q: \langle F(x),x- z\rangle\leq 0\;\forall z\in Q, \] where \(Q\) is a convex closed set in a real reflexive Banach space \(X\) and \(F\) is a monotone pointset mapping. An exact penalty method is proposed which enables on to remove functional constraints. The obtained result is used for constructing optimal iterative schemes for finding saddle points under functional constraints. No numerical examples are given.