On Bilevel Split Pseudomonotone Variational Inequality Problems with Applications
- 234 Downloads
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.
KeywordsSplit variational inequality Subgradient extragradient-Halpern method Pseudomonotone mapping Discrete optimal control problem
Mathematics Subject Classification (2010)47J25 47N10 90C25
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.
- 7.Censor, Y., Segal, A.: Iterative projection methods in biomedical inverse problems. In: Censor, Y, Jiang, M., Louis, A.K. (eds.) Mathematical Methods in Biomedical Imaging and Intensity-Modulated Therapy, IMRT, Edizioni della Norale, pp 65–96, Pisa (2008)Google Scholar
- 13.Goebel, K., Kirk, W.A.: Topics in metric fixed point theory. In: Cambridge Studies in Advanced Mathematics, vol. 28, Cambridge University Press (1990)Google Scholar