Autonomous Mobility-on-Demand (AMoD) systems require solving large-scale dynamic traffic assignment (DTA) problems under capacity and congestion constraints. Existing formulations are typically solved as large linear programs, limiting scalability in realistic transportation networks. This project develops a novel optimization framework that exploits the hidden network-flow structure of dynamic traffic assignment models. By combining a Conditional Gradient Augmented Lagrangian (CGAL) approach with specialized Minimum-Cost Concurrent Flow algorithms on time-expanded networks, the framework significantly reduces computational complexity while preserving solution quality. Experimental results demonstrate substantial runtime improvements over state-of-the-art LP solvers, enabling scalable optimization for large AMoD systems.