Duality Results for Generalized Vector Variational Inequalities with Set-Valued Maps |
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| Authors: | P. H. Sach D. S. Kim L. A. Tuan G. M. Lee |
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| Affiliation: | (1) Institute of Mathematics, Hanoi, Vietnam;(2) Department of Applied Mathematics, Pukyong National University, Pusan, Republic of Korea;(3) Ninh Thuan College of Pedagogy, Ninh Thuan, Vietnam |
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| Abstract: | In this paper, we introduce new dual problems of generalized vector variational inequality problems with set-valued maps and we discuss a link between the solution sets of the primal and dual problems. The notion of solutions in each of these problems is introduced via the concepts of efficiency, weak efficiency or Benson proper efficiency in vector optimization. We provide also examples showing that some earlier duality results for vector variational inequality may not be true. This work was supported by the Brain Korea 21 Project in 2006. |
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| Keywords: | Vector variational inequalities Set-valued maps Duality Conjugate maps Biconjugate maps |
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