Convex programming formulations of the asymmetric traffic assignment problem

Recently introduced optimization formulations of the asymmetric traffic assignment problem are developed. The duality of two formulations is shown, and conditions for convexity and differentiability of the objective functions are given. Convexity conditions are also given for the family of formulations recently introduced by Smith (1983). When the travel cost vector is affine and monotone, all of the formulations are shown to be convex programming problems. Algorithmic implications of the results are discussed.