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Uniqueness of supporting hyperplanes and an alternative to solutions of variational inequalities

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  • Songnian He
  • Hong-Kun Xu

Abstract

A uniqueness theorem of supporting hyperplanes for a class of convex level sets in a Hilbert space is obtained. As an application of this result, we prove an alternative theorem on solutions of variational inequalities defined on convex level sets. Three examples are given to demonstrate the usefulness and advantages of our alternative theorem. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Songnian He & Hong-Kun Xu, 2013. "Uniqueness of supporting hyperplanes and an alternative to solutions of variational inequalities," Journal of Global Optimization, Springer, vol. 57(4), pages 1375-1384, December.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:4:p:1375-1384
    DOI: 10.1007/s10898-012-9995-z
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    References listed on IDEAS

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    1. Yang, Hai & Bell, Michael G. H., 1997. "Traffic restraint, road pricing and network equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 31(4), pages 303-314, August.
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    Cited by:

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    2. Dilip Madan, 2015. "Asset pricing theory for two price economies," Annals of Finance, Springer, vol. 11(1), pages 1-35, February.

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