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Inexact proximal point method for general variational inequalities
Authors:Abdellah Bnouhachem  Muhammad Aslam Noor
Institution:a School of Management Science and Engineering, Nanjing University, Nanjing 210093, PR China
b Mathematics Department, COMSATS Institute of Information Technology, Islamabad, Pakistan
Abstract:In this paper, 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.
Keywords:Proximal point algorithms  Inexact criterion  General variational inequalities  Projection methods
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