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Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (3): 313-321.doi: https://doi.org/10.1007/s10483-009-0305-x

• Articles • 上一篇    下一篇

Generalized gap functions and error bounds for generalized variational inequalities

胡艳红,宋文   

  1. 1. Department of Mathematics, Northeast Normal University, Changchun 130024, P. R. China;
    2. Department of Mathematics, Harbin Normal University, Harbin 150080, P. R. China
  • 收稿日期:2008-03-18 修回日期:2008-12-22 出版日期:2009-03-05 发布日期:2009-03-01
  • 通讯作者: Wen SONG, Professor, Ph. D., E-mail:wsong@hrbnu.edu.cn E-mail:wsong@hrbnu.edu.cn

Generalized gap functions and error bounds for generalized variational inequalities

Yan-hong HU, Wen SONG   

  1. 1. Department of Mathematics, Northeast Normal University, Changchun 130024, P. R. China;
    2. Department of Mathematics, Harbin Normal University, Harbin 150080, P. R. China
  • Received:2008-03-18 Revised:2008-12-22 Online:2009-03-05 Published:2009-03-01
  • Contact: Wen SONG, Professor, Ph. D., E-mail:wsong@hrbnu.edu.cn E-mail:wsong@hrbnu.edu.cn

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摘要： We consider some classes of generalized gap functions for two kinds of generalized variational inequality problems. We obtain error bounds for the underlying variational inequalities using the generalized gap functions under the condition that the involved mapping F is g-strongly monotone with respect to the solution, but not necessarily continuous differentiable, even not locally Lipschitz.

关键词: variational inequality, gap functions, error bounds

Abstract: We consider some classes of generalized gap functions for two kinds of generalized variational inequality problems. We obtain error bounds for the underlying variational inequalities using the generalized gap functions under the condition that the involved mapping F is g-strongly monotone with respect to the solution, but not necessarily continuous differentiable, even not locally Lipschitz.

Key words: variational inequality, gap functions, error bounds

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