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].
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This work was supported by the National Natural Science Foundation of China and the Scientific Research Foundation for the Returned Overseas Chinese, Scholars, State Education Ministry.
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Huang, NJ., Li, J. On Vector Implicit Variational Inequalities and Complementarity Problems. J Glob Optim 34, 399–408 (2006). https://doi.org/10.1007/s10898-004-1938-x
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DOI: https://doi.org/10.1007/s10898-004-1938-x