LinearizeLLM: An Agent-Based Framework for LLM-Driven Exact Linear Reformulation of Nonlinear Optimization Problems

TL;DR

The results indicate that specialized LLM agents can automate linearization tasks, opening a path toward fully conversational modeling pipelines for nonlinear optimization.

Abstract

Reformulating nonlinear optimization problems is largely manual and expertise-intensive, yet it remains essential for solving such problems with linear optimization solvers or applying special-purpose algorithms. We introduce \textit{LinearizeLLM}, an agent-based framework that solves this task by leveraging Large Language Models (LLMs). The framework assigns each nonlinear pattern to a \textit{reformulation agent} that is explicitly instructed to derive an exact linear reformulation for its nonlinearity pattern, for instance, absolute-value terms or bilinear products of decision variables. The agents then coordinate to assemble a solver-ready linear model equivalent to the original problem. To benchmark the approach, we create a dataset of 20 real-world nonlinear optimization problems derived from the established ComplexOR dataset of linear optimization problems. We evaluate our approach with several LLMs. Our results indicate that specialized LLM agents can automate linearization tasks, opening a path toward fully conversational modeling pipelines for nonlinear optimization.

Figures (2)

• Figure 1: Illustration of the LinearizeLLM workflow
• Figure 2: Heat-map of OSR, DSR, RSR and CSR for six nonlinearity patterns when Gemini 2.5 Flash is prompted with full, partial or no context (left to right blocks). Darker cells indicate higher percentages.