Acta Mathematica Vietnamica

, Volume 38, Issue 4, pp 529–540 | Cite as

Algorithms for a class of bilevel programs involving pseudomonotone variational inequalities

  • Bui Van Dinh
  • Le Dung MuuEmail author


We propose algorithms for finding the projection of a given point onto the solution set of the pseudomonotone variational inequality problem. This problem arises in the Tikhonov regularization method for pseudomonotone variational inequality. Since the solution set of the variational inequality is not given explicitly, the available methods of mathematical programming and variational inequalities cannot be applied directly.


Bilevel variational inequality Pseudomonotonicity Projection method Armijo linesearch Convergence 

Mathematics Subject Classification (2010)

49M37 90C26 65K15 



We would like to thank the Associate Editor and the referees for their useful remarks and comments that helped us very much in revising the paper. This work is supported by the Vietnam National Foundation for Science Technology Development (NAFOSTED) under Grant 101-02-2011.19.


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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2013

Authors and Affiliations

  1. 1.Le Quy Don Technical UniversityHanoiVietnam
  2. 2.Institute of MathematicsVASTHanoiVietnam

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