Solvability of the Minty Variational Inequality

Yiran He ()
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Yiran He: Sichuan Normal University

Journal of Optimization Theory and Applications, 2017, vol. 174, issue 3, No 4, 686-692

Abstract: 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.

Keywords: Minty variational inequality; Quasimonotone mapping; Set-valued mapping; 47J20; 47H05 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-017-1124-1

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