A penalized nonlinear ADMM algorithm applied to the multi-constrained traffic assignment problem

We formulate the Multi-Constrained Dynamic Traffic Assignment (DTA) problem as an instance of the nonlinear composite problem. To solve the problem, this paper introduces then the penalized nonlinear alternating direction method of multipliers (ADMM), a numerical algorithm that combines the nonlinear ADMM algorithm with the external penalty method. Numerical results are then presented, analyzed and compared against those obtained by applying the Reformulation-Linearization Technique (RLT)-based convex relaxation method together with piecewise linear approximation of the objective function.