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Algorithms for a class of bilevel programs involving pseudomonotone variational inequalities

Abstract

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.

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Acknowledgements

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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Correspondence to Le Dung Muu.

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Dinh, B.V., Muu, L.D. Algorithms for a class of bilevel programs involving pseudomonotone variational inequalities. Acta Math Vietnam. 38, 529–540 (2013). https://doi.org/10.1007/s40306-013-0032-1

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Keywords

  • Bilevel variational inequality
  • Pseudomonotonicity
  • Projection method
  • Armijo linesearch
  • Convergence

Mathematics Subject Classification (2010)

  • 49M37
  • 90C26
  • 65K15