Solving non-additive traffic assignment problems: A descent method for co-coercive variational inequalities

This paper developed a descent direction of the merit function for co-coercive variational inequality (VI) problems. The descent approach is closely related to Fukushima's method for strongly monotone VI problems and He's method for linear VI problems, and can be viewed as an extension for the more general case of co-coercive VI problems. This extension is important for route-based traffic assignment problems as the associated VI is often neither strongly monotone nor linear. This study then implemented the solution method for traffic assignment problems with non-additive route costs. Similar to projection-based methods, the computational effort required per iteration of this solution approach is modest. This is especially so for traffic equilibrium problems with elastic demand, where the solution method consists of a function evaluation and a simple projection onto the non-negative orthant.