zbMATH — the first resource for mathematics

On vector variational inequalities: Application to vector equilibria. (English) Zbl 0892.90158
Summary: We motivate the study of a vector variational inequality by a practical flow equilibrium problem on a network, namely a generalization of the well-known Wardrop equilibrium principle. Both weak and strong forms of the vector variational inequality are discussed and their relationships to a vector optimization problem are established under various convexity assumptions.

90C29 Multi-objective and goal programming
49J40 Variational inequalities
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90B10 Deterministic network models in operations research
Full Text: DOI
[1] MAGNANTI, T. L., Models and Algorithms for Predicting Urban Traffic Equilibria, Transportation Planning Models, Edited by M. Florian, Elsevier Science Publishers, Amsterdam, Holland, pp. 153–185, 1984.
[2] FLORIAN, M., Nonlinear Cost Network Models in Transportation Analysis, Mathematical Programming Study, Vol. 26, pp. 167–196, 1986. · Zbl 0607.90029 · doi:10.1007/BFb0121092
[3] NAGURNEY, A., Network Economics: A Variational Inequality Approach, Kluwer Academic Publishers, Dordrecht, Netherlands, 1993. · Zbl 0873.90015
[4] CHEN, G. Y., and YEN, N. D., On the Variational Inequality Model for Network Equilibrium, Internal Report 3.196 (724), Department of Mathematics, University of Pisa, 1993.
[5] GIANNESSI, F., Theorems of the Alternative, Quadratic Programs, and Complementarity Problems, Variational Inequalities and Complementarity Problems, Edited by R. W. Cottle, F. Giannessi, and J. L. Lions, Wiley, New York, New York, pp. 151–186, 1980.
[6] CHEN, G. Y., and YANG, X. Q., The Vector Complementarity Problem and Its Equivalences with Weak Minimal Element, Journal of Mathematical Analysis and Applications, Vol. 153, pp. 136–158, 1990. · Zbl 0712.90083 · doi:10.1016/0022-247X(90)90223-3
[7] YANG, X. Q., Generalized Convex Functions and Vector Variational Inequalities, Journal of Optimization Theory and Applications, Vol. 799, pp. 563–580, 1993. · Zbl 0797.90085 · doi:10.1007/BF00940559
[8] YANG, X. Q., Vector Variational Inequality and Its Duality, Nonlinear Analysis: Theory, Methods and Applications, Vol. 21, pp. 869–877, 1993. · Zbl 0809.49009 · doi:10.1016/0362-546X(93)90052-T
[9] ORTEGA, J. M., and RHEINBOLDT, W. C., Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, New York, 1970. · Zbl 0241.65046
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.