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Improvements of some projection methods for monotone nonlinear variational inequalities. (English) Zbl 1025.65036
The authors study the relationships between the Goldstein-Levitin-Polyak projection method (explicit method), the proximal method (implicit method) and then the extragradient method of G. M. Korpelevich [Ekonom. i Mat. Metody 12, 747-756 (1976; Zbl 0342.90044)] for nonlinear variational inequalities. The last method can be referred to as a prediction-correction method which uses the explicit method in the prediction step and the implicit method in the correction step. The authors improve it by using better prediction and correction steps. Numerical experiments show that the improvements are significant.

MSC:
65K10Optimization techniques (numerical methods)
49J40Variational methods including variational inequalities
49M15Newton-type methods in calculus of variations