College of Science & Engineering
Bilevel optimization (BO), also known as two-level optimization, is an important branch within mathematical optimization. It plays a vital role in addressing hierarchical decision scenarios in a variety of fields, including machine learing, imaging science, signal processing, economics, supply chain, power system, and transportation. Its importance is growing rapidly as it provides robust solutions to increasingly complex real-world challenges, especially in machine learning. Solving BO problems is vastly challenging in general due to the nested nature and the need to consider multiple objectives and constraints simultaneously. Existing methods are only applicable to a narrow scope of BO problems, and many computational challenges remain to be addressed for BO. This project focuses on developing novel computational methods with complexity guarantees for solving a broad spectrum of challenging BO problems.