A variational approach for minimum cost flow problems

Abstract

SummaryWe consider a variational model for traffic network problems, which generalizes the classic minimum cost flow problem. This model has the peculiarity of being formulated by means of a suitable variational inequality. The Lagrangean approach to the study of this variational inequality allows us to consider dual variables associated with the constraints of the feasible set, and to generalize the classic Bellman optimality conditions in order to obtain a stopping criterion for a gap function algorithm.