Article

Journal of Optimization Theory and Applications

, Volume 123, Issue 3, pp 533-548

First online:

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

  • P. Q. KhanhAffiliated withDepartment of Mathematics and Computing Science, Vietnam National University
  • , L. M. LuuAffiliated withDepartment of Mathematics, University of Dalat

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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 inequalities topological vector spaces solution existence KKM mappings upper semicontinuity generalized lower hemicontinuity pseudomonotonicity quasicomplementarity problems traffic networks multivalued costs weak and strong equilibrium flows