We consider the time dependent traffic equilibrium problern 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.
CITATION STYLE
Khan, A., & Raciti, F. (2007). On Time Dependent Vector Equilibrium Problems. In Variational Analysis and Applications (pp. 579–587). Springer US. https://doi.org/10.1007/0-387-24276-7_35
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