On vector network equilibrium problems

Abstract

In this paper we define a concept of weak equilibrium for vector network equilibrium problems. We obtain sufficient conditions of weak equilibrium points and establish relation with vector network equilibrium problems and vector variational inequalities.

Keywords

Network equilibrium problem / vector variational inequality / weak equilibrium

References

[1] Brenninger-Göthe M., Jørnsten K., Lundgren J. T.. Estimation of origin-destination matrices from traffic counts using multiobjective programming formulations. Transp. Res., 1989, 23B: 257-270.

[2] Chen G. Y., Goh C. J., Yang X. Q.. Vector network equilibrium problems and nonlinear scalarization methods. Math. Meth. Oper. Res., 1999, 49: 239-253.

[3] Chen, G. Y. and N. D. Yen, “On the variational inequality model for network equilibrium”, Internal Report, Department of Mathematics, University of Pisa, 3. Vol. 196, No.724, 1993.

[4] Dial R. B.. Bicriteria traffic assignment: basic theory and elementary algorithms. Transp. Sci., 1996, 30: 93-111.

[5] Goh C. J., Yang X. Q.. On Minkowski metric and weighted Tchebyshev norm in vector optimization. Optimization, 1998, 43: 353-365.

[6] Leurent F.. Cost versus time equilibrium over a network. European J. Oper. Res., 1993, 71: 205-221.

[7] Nagurney A.. Network Economics, A Variational Inequality Approach, 1993, Dordrecht: Kluwer Academic Publishers.

[8] Wardrop J.. Some theoretical aspects of road traffic research. Proceeding of the Institute of Civil Engineers, 1952, 1: 325-378.

[9] Yang X. Q., Goh C. J.. On vector variational inequalities: application to vector equilibria. J. Optim. Theory Appl., 1997, 95: 431-443.