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Zbl 1101.49026
Bnouhachem, Abdellah; Noor, Muhammad Aslam
Inexact proximal point method for general variational inequalities. (English)
[J] J. Math. Anal. Appl. 324, No. 2, 1195-1212 (2006). ISSN 0022-247X

Summary: We suggest and analyze a new inexact proximal point method for solving general variational inequalities, which can be considered as an implicit predictor-corrector method. An easily measurable error term is proposed with further relaxed error bound and an optimal step length is obtained by maximizing the profit-function and is dependent on the previous points. Our results include several known and new techniques for solving variational inequalities and related optimization problems. Results obtained in this paper can be viewed as an important improvement and refinement of the previously known results. Preliminary numerical experiments are included to illustrate the advantage and efficiency of the proposed method.

MSC 2000:: *49M37 Methods of nonlinear programming type
49J40 Variational methods including variational inequalities

Keywords: proximal point algorithms; inexact criterion; general variational inequalities; projection methods

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Zentralblatt MATH Berlin [Germany]