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Acta Mathematica Vietnamica

, Volume 42, Issue 3, pp 413–429 | Cite as

On Bilevel Split Pseudomonotone Variational Inequality Problems with Applications

  • Pham Ky Anh
  • Tran Viet Anh
  • Le Dung MuuEmail author
Article

Abstract

In this paper, we investigate a bilevel split variational inequality problem (BSVIP) involving a strongly monotone mapping in the upper-level problem and pseudomonotone mappings in the lower-level one. A strongly convergent algorithm for such a BSVIP is proposed and analyzed. In particular, a problem of finding the minimum-norm solution of a split pseudomonotone variational inequality problem is also studied. As a consequence, we get a strongly convergent algorithm for finding the minimum-norm solution to the split feasibility problem, which requires only two projections at each iteration step. An application to discrete optimal control problems is considered.

Keywords

Split variational inequality Subgradient extragradient-Halpern method Pseudomonotone mapping Discrete optimal control problem 

Mathematics Subject Classification (2010)

47J25 47N10 90C25 

Notes

Acknowledgments

The first and the third authors are grateful to the Vietnam Institute for Advanced Study in Mathematics (VIASM) for providing them excellent working conditions. The third author is supported by NAFOSTED, grant 101-01-2014.24.

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2016

Authors and Affiliations

  1. 1.Department of MathematicsVietnam National UniversityThanh XuanVietnam
  2. 2.Department of Scientific FundamentalsPosts and Telecommunications Institute of TechnologyHanoiVietnam
  3. 3.Institute of MathematicsVASTHanoiVietnam

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