Optimization modeling

Optimization problems appear in industrial applications from manufacturing and distribution to healthcare. However, most such problems are still solved heuristically by hand rather than optimally by state-of-the-art solvers, as the expertise required to formulate and solve these problems limits the widespread adoption of optimization tools and techniques. My work has developed several tools to simplify optimization modeling. Most recently, we released a Large Language Model (LLM)-based agent to formulate and solve MILP problems from natural language descriptions.

Talks

Software

Papers

Algebraic characterization of equivalence between optimization algorithms
L. Lessard and M. Udell
2025
[arxiv][url][bib]

OptiMUS-0.3: Using Large Language Models to Model and Solve Optimization Problems at Scale
A. AhmadiTeshnizi, W. Gao, H. Brunborg, S. Talaei, and M. Udell
Submitted, 2024
[arxiv][url][bib]

OptiMUS: Scalable Optimization Modeling Using MIP Solvers and Large Language Models
A. AhmadiTeshnizi, W. Gao, and M. Udell
International Conference on Machine Learning (ICML), 2024
[arxiv][url][bib][video]

OptiMUS: Optimization Modeling Using MIP Solvers and Large Language Models
A. AhmadiTeshnizi, W. Gao, and M. Udell
2023
[arxiv][url][bib][video]

An automatic system to detect equivalence between iterative algorithms
S. Zhao, L. Lessard, and M. Udell
2021
[arxiv][pdf][url][slides][bib]

Disciplined Multi-Convex Programming
X. Shen, S. Diamond, M. Udell, Y. Gu, and S. Boyd
Chinese Control and Decision Conference (CCDC), 2017
Best Student Paper
[arxiv][bib]

Convex Optimization in Julia
M. Udell, K. Mohan, D. Zeng, J. Hong, S. Diamond, and S. Boyd
SC14 Workshop on High Performance Technical Computing in Dynamic Languages, 2014
[arxiv][url][code][bib]