Variational inequalities on weakly compact sets

Authors:
Y. Chiang
Affiliations:
Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan, ROC 80424
Venue:
Journal of Global Optimization
Year:
2010

Citing 3
Cited 1

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Duality in Multivalued Complementarity Theory by Using Inversions and Scalar Derivatives

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Topological Methods in Complementarity Theory (Nonconvex Optimization and Its Applications)

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Characterizations for solidness of dual cones with applications

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Abstract

In this paper, we derive an existence result for generalized variational inequalities associated with multivalued mappings on weakly compact sets under a continuity assumption which is much weaker than the regular complete continuity. As an application, we prove the existence of exceptional families of elements for such mappings on closed convex cones in reflexive Banach spaces when the corresponding complementarity problems have no solutions.