The field of graph-based optimization and control is witnessing significant developments, with a focus on innovative numerical schemes and algorithmic frameworks. Researchers are exploring new methods to solve complex problems, such as Hamilton-Jacobi equations on Wasserstein spaces, discrete evacuation models, and multi-population Wardrop equilibria. These advancements have the potential to impact various applications, including traffic management, network design, and target interception. Noteworthy papers in this area include:

• A study on finite difference schemes for Hamilton-Jacobi equations on Wasserstein spaces, which proposes novel numerical schemes and establishes their convergence and accuracy.
• A paper on discrete evacuation in graphs with multiple exits, which provides an algorithmic framework for constructing valid evacuation strategies with constant competitive ratios.
• A work on Hessian Riemannian flow for multi-population Wardrop equilibrium, which introduces a novel numerical method for optimizing flows on generalized graphs.
• A research on traffic-oblivious multi-commodity flow network design, which presents a tight approximation algorithm for the Minimum Multi-Commodity Flow Subgraph problem.