Abstract
In this paper, a (weak) vector equilibrium principle for vector network problems with capacity constraints and elastic demands is introduced. A sufficient condition for a (weak) vector equilibrium flow to be a solution for a system of (weak) vector quasi-variational inequalities is obtained. By virtue of Gerstewitz’s nonconvex separation functional ξ, a (weak) ξ-equilibrium flow is introduced. Relations between a weak vector equilibrium flow and a (weak) ξ-equilibrium flow is investigated. Relations between weak vector equilibrium flows and two classes of variational inequalities are also studied.
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References
Chen, G.Y., Yen, N.D.: On the variational inequality model for network equilibrium. Internal Report 3.196 (724), Department of Mathematics, University of Pisa, Pisa (1993).
Chen G.Y., Goh C.J., Yang X.Q. (1999). Vector network equilibrium problems and nonlinear scalarization methods. Math. Methods Oper. Res. 49:239–253
Cheng, T.C.E., Wu, Y.N.: A multiclass, multicriteria supply-demand network equilibrium model, preprint
Daniele P., Maugeri A. (2002). Variational inequalities and discrete and continuum models of network equilibrium problems. Math. Comput. Model 35:689–708
Daniele P., Maugeri A., Oettli W. (1999). Time-dependent traffic equilibria. J. Optim. Theory Appl. 103:543–555
Daniele P., Maugeri A., Oettli W. (1998). Variational inequalities and time-dependent traffic equilibria. C. R. Acad. Sci. Paris Sér. I Math. 326:1059–1062
Gerth C., Weidner P. (1990). Nonconvex separation theorems and some applications in vector optimization. J. Optim. Theory Appl. 67:297–320
Giannessi, F., Maugeri, A.: Variational inequalities and network equilibrium problems. In: Proceedings of the Conference Held in Erice, Plenum Press, New York 1994
Giannessi F. (2000). Vector Variational Inequalities and Vector Equilibria. Kluwer Academic Publisher, Dordrecht
Goh C.J., Yang X.Q. (1999). Theory and methodology of vector equilibrium problem and vector optimization. Eur. J. Oper. Res. 116:615–628
Li, S.J., Teo, K.L., Yang, X.Q.: A remark on a standard and linear vector network equilibrium problem with capacity constraints. Eur. J. Oper. Res. (online)
Mageri A. (1995). Variational and quasi-variational inequalities in network flow models. In: Giannessi F., Maugeri A. (eds) Recent developments in theory and algorithms, Variational inequalities and network equilibrium problems. Plenum Press, New York, pp. 195–211
Nagurney A. (1999). Network Economics, A Variational Inequality Approach. Kluwer Academic Publishers, Dordrecht
Nagurney A. (2000). A multiclass, multicriteria traffic network equilibrium model. Math. Comp. Model. 32:393–411
Nagurney A., Dong J. (2002). A multiclass, multicriteria traffic network equilibrium model with elastic demand. Transpor. Res. Part B 36:445–469
Yang X.Q., Goh C.J. (1997). On vector variational inequalities: application to vector equilibria. J. Optim. Theory Appl. 95:431–443
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Li, S.J., Teo, K.L. & Yang, X.Q. Vector equilibrium problems with elastic demands and capacity constraints. J Glob Optim 37, 647–660 (2007). https://doi.org/10.1007/s10898-006-9078-0
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DOI: https://doi.org/10.1007/s10898-006-9078-0