Airline Competitive Hub-and-Spoke Network Design by Reweighted Norm-1

Air transportation networks are critical components of modern transport systems, enabling rapid connectivity across vast regions. This study presents a novel convex optimization methodology for designing and optimizing air transportation networks. Unlike traditional mixed-integer nonlinear programming approaches, which struggle with scalability and complexity, our method leverages sparsity-promoting regularizers and entropy-based regularizers to optimize the selection of routes and hub capacities while accounting for infrastructure costs and user behavior using a logit model. The proposed method achieves near-optimal solutions with significantly reduced computation times, making it practical for large-scale networks. Application to a real-world U.S. domestic air network demonstrates its effectiveness, providing high-quality solutions, and enabling robust decision-making. These results highlight the potential of convex optimization in advancing air network design, paving the way for future extensions, including probabilistic models and multilevel optimization.