Abstract
We consider the existence of solutions to the Minty variational inequality, as it plays a key role in a projection-type algorithm for solving the variational inequality. It is shown that, if the underlying mapping has a separable structure with each component of the mapping being quasimonotone, then the Minty variational inequality has a solution. An example shows that the underlying mapping itself is not necessarily quasimonotone, although each of its components is.
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Acknowledgements
The author would like to thank Professor Franco Giannessi and the referees for valuable suggestions. This work was partially supported by National Natural Science Foundation of China under Grant 11271274.
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Communicated by Antonino Maugeri.
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He, Y. Solvability of the Minty Variational Inequality. J Optim Theory Appl 174, 686–692 (2017). https://doi.org/10.1007/s10957-017-1124-1
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DOI: https://doi.org/10.1007/s10957-017-1124-1