First-Order Methods for Bilevel Optimization

Zhaosong Lu is a Full Professor in the Department of Industrial and Systems Engineering at the University of Minnesota. He received his Ph.D. in Operations Research from Georgia Institute of Technology. His research focuses on the theory and algorithms of continuous optimization, with applications in data science and machine learning. Dr. Lu has published extensively in leading journals such as Mathematical Programming, Mathematics of Operations Research, and SIAM Journal on Optimization. His work has been supported by funding agencies including AFOSR, NSF, and ONR. He has served on several prize committees, such as the INFORMS George Nicholson Prize and the ICCOPT Best Paper Award. In addition, he has served as an Associate Editor for journals including SIAM Journal on Optimization, Computational Optimization and Applications, and Journal of Global Optimization.

Bilevel optimization, also known as two-level optimization, is an important branch within mathematical optimization. It has found applications across various domains, including economics, logistics, supply chain, transportation, engineering design, and machine learning. In this talk, we will present first-order methods for solving a class of bilevel optimization problems using either single or sequential minimax optimization schemes. We will discuss the first-order oracle complexity of these methods and present preliminary numerical results to illustrate their performance. This is joint work with Sanyou Mei (HKUST).

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