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.
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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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Anh, P.K., Anh, T.V. & Muu, L.D. On Bilevel Split Pseudomonotone Variational Inequality Problems with Applications. Acta Math Vietnam 42, 413–429 (2017). https://doi.org/10.1007/s40306-016-0178-8
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DOI: https://doi.org/10.1007/s40306-016-0178-8
Keywords
- Split variational inequality
- Subgradient extragradient-Halpern method
- Pseudomonotone mapping
- Discrete optimal control problem