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

Songnian He () and Hong-Kun Xu ()

Journal of Global Optimization, 2013, vol. 57, issue 4, 1375-1384

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

Keywords: Supporting hyperplane; Uniqueness; Variational inequality; Alternative; Hilbert space; 47J20; 49J20; 90C25 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10898-012-9995-z

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