×

On existence of vector equilibrium flows with capacity constraints of arcs. (English) Zbl 1192.90211

Summary: We propose a (weak) vector equilibrium principle with capacity constraints of arcs. By proving the existence of solutions for the weighted variational inequality, we establish the existence results of (weak) vector traffic equilibrium flows with capacity constraints of arcs.

MSC:

90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Wardrop, J., Some theoretical aspects of road traffic research, Proceedings of the institute of civil engineers, part II, 1, 325-378, (1952)
[2] G.Y. Chen, N.D. Yen, On the variational inequality model for network equilibrium, Internal Report 3. 196 (724), Department of Mathematics, University of Pisa, 1993
[3] Khanh, P.Q.; Luu, L.M., On the existence of solutions to vector quasivariational inequalities and quasicomplementarity problems with applications to traffic network equilibria, Journal of optimization theory and applications, 123, 533-548, (2004) · Zbl 1059.49017
[4] Khanh, P.Q.; Luu, L.M., Some existence results for quasi-variational inequalities involving multifunctions and applications to traffic equilibrium problems, Journal of global optimization, 32, 551-568, (2005) · Zbl 1097.49012
[5] Z. Lin, The study of traffic equilibrium problems with capacity constraints of arcs, Nonlinear Analysis: Real World Applications (in press) · Zbl 1198.90085
[6] Chen, G.Y., On vector network equilibrium problems, Journal of systems science and systems engineering, 14, 454-461, (2005)
[7] Giannessi, F., Vector variational inequalities and vector equilibria, (2000), Kluwer Academic Publisher · Zbl 0952.00009
[8] Goh, C.J.; Yang, X.Q., Vector equilibrium problem and vector optimization, European journal of operational research, 116, 615-628, (1999) · Zbl 1009.90093
[9] Li, S.J.; Chen, G.Y., On relations between multiclass multicriteria traffic network equilibrium models and vector variational inequalities, Journal of systems science and systems engineering, 15, 284-297, (2006)
[10] Li, S.J.; Teo, K.L.; Yang, X.Q., A remark on a standard and linear vector network equilibrium problem with capacity constraints, European journal of operational research, 184, 13-23, (2008) · Zbl 1175.90068
[11] Li, S.J.; Yang, X.Q.; Chen, G.Y., A note on vector network equilibrium principles, Mathematical methods of operations research, 64, 327-334, (2006) · Zbl 1131.90010
[12] Yang, X.Q.; Goh, C.J., On vector variational inequalities: application to vector equilibria, Journal of optimization theory and applications, 95, 431-443, (1997) · Zbl 0892.90158
[13] Anaari, Q.H.; Khan, Z.; Siddiqi, A.H., Weighted variational inequalities, Journal of optimization theory and applications, 127, 2, 263-283, (2005) · Zbl 1108.49004
[14] Cubiotti, Paolo, Existence of generalised Pareto equilibria for constrained multiobjective games, International game theory review, 2, 4, 329-344, (2000) · Zbl 0992.91005
[15] Wang, S.Y., Existence of a Pareto equilibrium, Journal of optimization theory and applications, 79, 373-384, (1993) · Zbl 0797.90124
[16] Yu, J.; Yuan, G.X.-Z., The study of Pareto equilibria for multiobjective games by fixed point and Ky Fan minimax inequality methods, Computers & mathematics with applications, 35, 17-24, (1998) · Zbl 1005.91008
[17] Browder, F.E., The fixed point theory of multi-valued mappings in topological vector spaces, Mathematische annalen, 177, 283-301, (1968) · Zbl 0176.45204
[18] Fan, K., A generalization of tychonoff’s fixed point theorem, Mathematische annalen, 142, 305-310, (1961) · Zbl 0093.36701
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.