Journal of Optimization Theory and Applications

, Volume 123, Issue 3, pp 533–548

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

  • P. Q. Khanh
  • L. M. Luu

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


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

Authors and Affiliations

  • P. Q. Khanh
    • 1
  • L. M. Luu
    • 2
  1. 1.Department of Mathematics and Computing ScienceVietnam National UniversityVietnam
  2. 2.Department of MathematicsUniversity of DalatVietnam