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This talk aims to respond to the question: are the classical mathematical optimization/game models, theories, and algorithms remaining valuable in the AI and LLM era? We present several cases to show how mathematical programming and AI/Machine-Learning technologies complement each other. In particular, we describe how classic optimization theories can be applied to accelerate the Gradient Methods that is popularly used for LLM Training and Fine-Tuning. On the other hand, we show advances in LP, SDP and/or Market-Equilibrium computing aided by Machine Learning techniques, First-Order methods and the GPU Implementations.

Yinyu Ye, formally the K.T. Li Professor of Stanford University, is now the Visiting Professor of Hong Kong University of Science and Technology, Shanghai Jiao Tong University and Chinese University of Hong Kong at Shenzhen. His current research topics include Continuous and Discrete Optimization, Data Science and Applications, Numerical Algorithm Design and Analyses, Algorithmic Game/Market Equilibrium, Operations Research and Management Science etc.; and he was one of the pioneers on Interior-Point Methods, Conic Linear Programming, Distributionally Robust Optimization, Online Linear Programming and Learning, Algorithm Analyses for Reinforcement Learning&Markov Decision Process and nonconvex optimization, and etc. He and his students have received numerous scientific awards, himself including the 2006 INFORMS Farkas Prize (Inaugural Recipient) for fundamental contributions to optimization, the 2009 John von Neumann Theory Prize for fundamental sustained contributions to theory in Operations Research and the Management Sciences, the inaugural 2012 ISMP Tseng Lectureship Prize for outstanding contribution to continuous optimization (every three years), the 2014 SIAM Optimization Prize awarded (every three years), etc.

叶荫宇 (Yinyu Ye), 原斯坦福大学李国鼎讲席教授，现任香港科技大学，上海交 通大学 和香港中文大学深圳访问讲习教授。他的主要研究方向为连续和离散优 化，数据科学及应用，数字算法设计及分析，算法博弈及市场均衡，运筹及管 理科学等; 他和其他科学家开创了内点优化算法，锥规划模型，分布式鲁棒优 化，在线线性规划和学习，强化学习和马可夫过程及非凸优化算法分析等。他 和他的学生多次获得科学奖项: 包括他自己的2006 INFORMS Farkas Prize (首 位获奖者) ，2009年约翰·冯·洛伊曼理论奖，国际数学规划2012 Tseng Lectureship Prize (首位获奖者每三年) ，2014美国应用数学学会优化奖 (每三年) 等。