# On the Existence of Solutions to Vector Quasivariational Inequalities and Quasicomplementarity Problems with Applications Break to Traffic Network Equilibria

Article

DOI: 10.1007/s10957-004-5722-3

- Cite this article as:
- Khanh, P.Q. & Luu, L.M. Journal of Optimization Theory and Applications (2004) 123: 533. doi:10.1007/s10957-004-5722-3

## Abstract

For vector quasivariational inequalities involving multifunctions in topological vector spaces, an existence result is obtained without a monotonicity assumption and with a convergence assumption weaker than semicontinuity. A new type of quasivariational inequality is proposed. Applications to quasicomplementarity problems and traffic network equilibria are considered. In particular, definitions of weak and strong Wardrop equilibria are introduced for the case of multivalued cost functions.

Vector quasivariational inequalitiestopological vector spacessolution existenceKKM mappingsupper semicontinuitygeneralized lower hemicontinuitypseudomonotonicityquasicomplementarity problemstraffic networksmultivalued costsweak and strong equilibrium flows

## Copyright information

© Springer Science+Business Media, Inc. 2004