Abstract
In this note we introduce the concept of vector network equilibrium flows when the ordering cone is the union of finitely many closed and convex cones. We show that the set of vector network equilibrium flows is equal to the intersection of finitely many sets, where each set is a collection of vector equilibrium flows with respect to a closed and convex cone. Sufficient and necessary conditions for a vector equilibrium flow are presented in terms of scalar equilibrium flows.
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This paper was supported in part by The Hong Kong Polytechnic University under grant number G-YF17. Cheng was also supported by the Research Grants Council of Hong Kong under grant number PolyU 5135/06E, Li was also supported by the National Natural Science Foundation of China (Grant number: 60574073) and the Natural Science Foundation Project of CQ CSTC (Grant number: 2007BB6117) and Yang was also supported by the National Natural Science Foundation of China (Grant number: 10831009).
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Cheng, T.C.E., Li, S.J. & Yang, X.Q. Vector equilibrium flows with nonconvex ordering relations. J Glob Optim 46, 537–542 (2010). https://doi.org/10.1007/s10898-009-9437-8
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DOI: https://doi.org/10.1007/s10898-009-9437-8