LinearizeLLM: An Agent-Based Framework for LLM-Driven Exact Linear Reformulation of Nonlinear Optimization Problems
Abstract
Reformulating nonlinear optimization problems into solver-ready linear optimization problems is often necessary for practical applications, but the process is often manual and requires domain expertise. We propose LinearizeLLM, an agent-based LLM framework that produces solver-ready linear reformulations of nonlinear optimization problems. Agents first detect the nonlinearity pattern (e.g., bilinear products) and apply nonlinearity pattern-aware reformulation techniques, selecting the most suitable linearization technique. We benchmark on 40 instances: 27 derived from ComplexOR by injecting exactly-linearizable operators, and 13 automatically generated instances with deeply nested nonlinearities. LinearizeLLM achieves 73\% mean end-to-end overall success (OSR) across nonlinearity depths (8.3x higher than a one-shot LLM baseline; 4.3x higher than Pyomo). The results suggest that a set of pattern-specialized agents can automate linearization, supporting natural-language-based modeling of nonlinear optimization.
Cite
@article{arxiv.2510.15969,
title = {LinearizeLLM: An Agent-Based Framework for LLM-Driven Exact Linear Reformulation of Nonlinear Optimization Problems},
author = {Paul-Niklas Ken Kandora and Simon Caspar Zeller and Aaron Jeremias Elsing and Elena Kuss and Steffen Rebennack},
journal= {arXiv preprint arXiv:2510.15969},
year = {2026}
}
Comments
This version is a major revision with a new abstract, updated workflow logic and description, an expanded instance set, additional numerical experiments, and corrected bibliography entries