Solving nonadditive traffic assignment problems: A self-adaptive projection-auxiliary problem method for variational inequalities
Gang Qian, Deren Han, Lingling Xu, Hai Long Yang · Journal of Industrial and Management Optimization · 2012
In the last decade, as calibrations of the classical trafficequilibrium problems, various models of traffic equilibrium problemswith nonadditive route costs have been proposed. For solving suchmodels, this paper develops a self-adaptive projection-auxiliaryproblem method for monotone variational inequality (VI) problems. Itfirst converts the original problem where the feasible set is theintersection of a linear manifold and a simple set to an augmentedVI with simple set, which makes the projection easy to implement.The self-adaptive strategy avoids the difficult task of choosing`suitable' parameters, and leads to fast convergence. Under suitableconditions, we prove the global convergence of the method. Somepreliminary computational results are presented to illustrate theability and efficiency of the method.