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Zbl 1059.49017
Phan Quoc Khanh; Le Minh Luu
On the existence of solutions to vector quasivariational inequalities and quasicomplementarity problems with applications to traffic network equilibria. (English)
[J] J. Optimization Theory Appl. 123, No. 3, 533-548 (2004). ISSN 0022-3239; ISSN 1573-2878/e

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 2000:: *49J40 Variational methods including variational inequalities
47J20 Inequalities involving nonlinear operators
47N10 Appl. of operator theory in optimization, math. programming, etc.
90B20 Highway traffic
90B10 Flows in networks
90C33 Complementarity problems

Keywords: vector quasivariational inequalities; topological vector spaces; KKM mappings; upper semicontinuity; generalized lower hemicontinuity; pseudomonotonicity; quasicomplementarity problems; traffic networks; weak and strong equilibrium flows

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