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He, B. S.; Liao, L. Z.

Improvements of some projection methods for monotone nonlinear variational inequalities. (English) Zbl 1025.65036

J. Optimization Theory Appl. 112, No. 1, 111-128 (2002).
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.
Reviewer: Dinh Nho Hao (Brussel)

Cited in 3 Reviews
Cited in 134 Documents

MSC:

65K10 Numerical optimization and variational techniques
49J40 Variational inequalities
49M15 Newton-type methods

Keywords:

Goldstein-Levitin-Polyak projection method; explicit method; proximal method; implicit method; extragradient method; nonlinear variational inequalities; prediction-correction method; numerical experiments

Citations:

Zbl 0342.90044
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Full Text: DOI

References:

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