On Time Dependent Vector Equilibrium Problems
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 wordsTime Dependent Traffic Networks Vector Variational Inequalities Pareto optimization multicriteria equilibrium problems quasi interior
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