MOA2026 | Short Course

Short Course 1

Speaker: Zhaosong Lu (University of Minnesota, USA)
Time: 14:30-16:00, June 26, 2026
Title: First-Order Methods for Bilevel and Minimax Optimization
Abstract: Bilevel and minimax optimization are two fundamentally important areas of modern mathematical optimization. They have found numerous applications in machine learning, artificial intelligence, data science, operations research, and engineering. In this short course, we will present recent developments in first-order methods for general bilevel and minimax optimization problems. In particular, we will introduce penalty and augmented Lagrangian frameworks that transform these problems into either a single structured minimax problem or a sequence of structured minimax subproblems. We will then discuss scalable first-order methods for solving the resulting problems and present their first-order operation complexity. Finally, we will provide preliminary numerical results to illustrate their performance.

Speaker: Zaiwen Wen (Peking University, China)
Time: 16:15–17:45, June 26, 2026
Title: Exploring Learning-Based Algorithms and Theories in Mathematical Optimization
Abstract: In this talk, we explore emerging paradigms that integrate data, models, algorithms, and theory in mathematical optimization. We first discuss the construction of mathematical optimization datasets with the assistance of large language models, focusing on adaptive modeling and structural extraction tailored to problem structures and application scenarios. We then present AI-driven optimization algorithms, including ODE-based learning-to-optimize methods, Monte Carlo policy optimization algorithms for binary integer programming, path-planning problems, and learning-based optimization approaches for DAG heterogeneous scheduling and quadratic assignment problems. Finally, we discuss the vision of advancing automated theorem proving by formalizing knowledge bases through mathematical optimization.