Mathematical Optimization in the Era of AI

How is artificial intelligence transforming mathematical optimization, and how can optimization improve AI systems themselves? At the 2026 INFORMS Annual Meeting in San Francisco, Yinyu Ye explored this two-way relationship in his keynote address, “Mathematical Optimization in the Era of AI.” 

The 2009 John von Neumann Theory Prize recipient and K.T. Li Professor Emeritus of Stanford University, Ye is now the Visiting Professor of Shanghai Jiao Tong University, Shanghai Institute of Mathematical and Interdisciplinary Sciences. His keynote address highlighted advances in classical optimization through online learning, first-order algorithms, low-rank representations, and GPU computing, alongside emerging applications in large language models (LLMs).

Accelerating Classical Optimization

Ye illustrated remarkable progress in solving large-scale optimization problems using the historically challenging linear programming instance zib03, which contains approximately 29 million variables and 20 million constraints. Solving this instance required 139 days in 2009, Ye said, whereas recent GPU-accelerated approaches reported solution times of approximately one minute in 2026.

Ye also discussed the importance of online learning techniques that adapt scaling parameters during optimization and first-order methods that exploit GPU parallelism to improve computational efficiency.

The Importance of Mathematical Structure

A central message of Ye’s address was the importance of exploiting mathematical structure. He discussed low-rank semidefinite programming methods that reduce computational and memory requirements. In quantum chemistry applications, exploiting cyclic symmetry in hydrogen systems reduced the number of optimization variables from quadratic to linear growth with problem size. In summarizing this principle, Ye said, “Always explore the data structure of the problem.”

AI as an Optimization Assistant

Ye also examined whether LLMs could replace traditional optimization solvers. In experiments involving 40 linear programming instances, a standalone LLM solved 16 optimally, whereas a conventional solver solved all 40 in 8.17 seconds. An LLM-assisted solver also solved all instances, but it required approximately six minutes to do so. Ye concluded, “LLMs cannot replace optimization solvers (yet).”

Nevertheless, LLMs demonstrated potential for discovering reusable strategies in mixed-integer programming. Experiments on 217 open MIPLIB instances reported that 52 instances proved optimal or infeasible and 59 improvements in primal bounds. These findings suggest that AI can complement traditional optimization methods by identifying problem-specific structures and strategies.

Optimization for LLMs

Beyond showing how AI can be used to assist optimization, Ye also demonstrated how optimization can improve AI systems themselves. One important application he discussed involves an online linear programming formulation for LLM serving. The model supports decisions about assigning incoming requests to available computing resources, while also accounting for workload imbalances and system performance. Ye presented optimization-based routing approaches, including BalanceRoute, to improve resource allocation and reduce delays. Reported results showed a 45.8% reduction in average end-to-end latency compared with round-robin routing. A deployment in Huawei’s Model-as-a-Service system also reported throughput improvements of approximately 14–15%.

Ye’s presentation demonstrated the complementary relationship between AI and mathematical optimization: While AI offers new opportunities for discovering effective optimization strategies, mathematical optimization remains essential for developing efficient, scalable, and reliable AI systems.