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An exact penalty method for monotone variational inequalities and order optimal algorithms for finding saddle points. (English. Russian original) Zbl 1230.65073
Russ. Math. 55, No. 8, 19-27 (2011); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2011, No. 8, 23-33 (2011).
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.

65K15 Numerical methods for variational inequalities and related problems
Full Text: DOI
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