On Vector Implicit Variational Inequalities and Complementarity Problems

Authors:
Nan-Jing Huang;Jun Li
Affiliations:
Department of Mathematics, Sichuan University, Chengdu, PR China 610064;Department of Mathematics, China West Normal University, Nanchong, PR China 637002
Venue:
Journal of Global Optimization
Year:
2006

Citing 4
Cited 2

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Abstract

In this paper, two vector implicit variational inequalities and three vector implicit complementarity problems are introduced with a more general order in ordered Banach spaces and the equivalence between them is studied under certain assumptions. Furthermore, some existence theorems of the vector implicit variational inequalities are proved. We answered the open question proposed by Rapcsák [Nonconvex Optim., Appl., Vol. 38, Kluwer Acad. Publ., Dordrecht, 2000, pp. 371---380].