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Solvability of the Minty Variational Inequality

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  • Yiran He

    (Sichuan Normal University)

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.

Suggested Citation

  • Yiran He, 2017. "Solvability of the Minty Variational Inequality," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 686-692, September.
    • Handle: RePEc:spr:joptap:v:174:y:2017:i:3:d:10.1007_s10957-017-1124-1
    DOI: 10.1007/s10957-017-1124-1
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    References listed on IDEAS

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    1. D. Aussel & N. Hadjisavvas, 2004. "On Quasimonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 121(2), pages 445-450, May.
    2. M. Bianchi & N. Hadjisavvas & S. Schaible, 2004. "Minimal Coercivity Conditions and Exceptional Families of Elements in Quasimonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 122(1), pages 1-17, July.
    3. I. V. Konnov, 1998. "On Quasimonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 99(1), pages 165-181, October.
    4. Minglu Ye & Yiran He, 2015. "A double projection method for solving variational inequalities without monotonicity," Computational Optimization and Applications, Springer, vol. 60(1), pages 141-150, January.
    5. Y. J. Wang & N. H. Xiu & C. Y. Wang, 2001. "Unified Framework of Extragradient-Type Methods for Pseudomonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 111(3), pages 641-656, December.
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    Cited by:

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    2. Jolaoso, Lateef O. & Shehu, Yekini & Yao, Jen-Chih, 2022. "Inertial extragradient type method for mixed variational inequalities without monotonicity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 353-369.

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