On Time Dependent Vector Equilibrium Problems

  • A. Khan
  • F. Raciti
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 79)


We consider the time dependent traffic equilibrium problem in the case of a vector valued cost operator. The motivation for this approach is that users can decide to choose a path according to several criteria. In fact, they may want to choose a minimum delay path as well as a minimum tax path. Other criteria can be introcuced in the model, depending on the particular problem under consideration. Thus, we are led to a multicriteria equilibrium problem which can be related to vector variational inequalities. The functional setting is the space L 2([0, T], R n). The extension of the definition of weak equilibria in such a space is not straightforward due to the fact that the cone made up of the non-negative functions has empty interior. We overcome this problem by using the notion of quasi interior of a closed convex set of a Hilbertspace and give sufficient conditions for the existence of weak equilibria.

Key words

Time Dependent Traffic Networks Vector Variational Inequalities Pareto optimization multicriteria equilibrium problems quasi interior 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • A. Khan
    • 1
  • F. Raciti
    • 2
    • 3
  1. 1.Department of Mathematical Sciences, Fisher HallMichigan Technological UniversityHoughtonUSA
  2. 2.Dipartimento di Matematica e InformaticaUniversità di CataniaCataniaItaly
  3. 3.Facoltà di Ingegneria dell’ Università di CataniaCataniaItaly

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