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Zbl 1068.65087
He, Bing-sheng; Yang, Zhen-hua; Yuan, Xiao-ming
An approximate proximal-extragradient type method for monotone variational inequalities. (English)
[J] J. Math. Anal. Appl. 300, No. 2, 362-374 (2004). ISSN 0022-247X

One of the most known approaches to constructing solution methods for monotone variational inequalities consists in incorporating a predictor step for computing parameters of a separating hyperplane and for providing the Fejér-monotone convergence. This approach is also known as combined relaxation; see {\it I. V.~Konnov} [Russ. Mathem. (Iz. VUZ), 37, No. 2, 44--51 (1993; Zbl 0835.90123)] and can be extended in several directions.\par {\it M. V. Solodov} and {\it B. F. Svaiter} [Math. Progr. 88, 371--389 (2000; Zbl 0963.90064)] proposed an inexact proximal point iteration as the predictor step. The authors suggest a modification of this method which involves an additional projection iteration for completing the predictor step. The method possesses the same convergence properties. Some results of numerical experiments on a network equilibrium problem are reported.
[Igor V. Konnov (Kazan)]

MSC 2000:: *65K10 Optimization techniques (numerical methods)
49J40 Variational methods including variational inequalities
49M20 Methods of relaxation type

Keywords: variational inequalities; monotone mappings; inexact proximal point methods; combined relaxation; convergence; numerical experiments; network equilibrium problem

Citations: Zbl 0835.90123; Zbl 0963.90064

Cited in: Zbl 1149.65050

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