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On the existence of solutions to vector quasivariational inequalities and quasicomplementarity problems with applications to traffic network equilibria. (English) Zbl 1059.49017
Summary: 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.
MSC:
49J40Variational methods including variational inequalities
47J20Inequalities involving nonlinear operators
47N10Applications of operator theory in optimization, convex analysis, programming, economics
90B20Traffic problems
90B10Network models, deterministic (optimization)
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
References:
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