NC2C: Automated Convexification of Generic Non-Convex Optimization Problems

TL;DR

This paper introduces NC2C, an LLM-based framework that automates the convexification of non-convex optimization problems, reducing manual effort and enabling efficient solutions with high success rates.

Contribution

The paper presents a novel automated framework using large language models to transform generic non-convex problems into convex forms, integrating symbolic reasoning and iterative validation.

Findings

Achieves 89.3% execution rate on diverse problems.

Attains 76% success rate in feasible convex transformations.

Outperforms baseline methods significantly.

Abstract

Non-convex optimization problems are pervasive across mathematical programming, engineering design, and scientific computing, often posing intractable challenges for traditional solvers due to their complex objective functions and constrained landscapes. To address the inefficiency of manual convexification and the over-reliance on expert knowledge, we propose NC2C, an LLM-based end-to-end automated framework designed to transform generic non-convex optimization problems into solvable convex forms using large language models. NC2C leverages LLMs' mathematical reasoning capabilities to autonomously detect non-convex components, select optimal convexification strategies, and generate rigorous convex equivalents. The framework integrates symbolic reasoning, adaptive transformation techniques, and iterative validation, equipped with error correction loops and feasibility domain correction mechanisms to ensure the robustness and validity of transformed problems. Experimental results on a diverse dataset of 100 generic non-convex problems demonstrate that NC2C achieves an 89.3\% execution rate and a 76\% success rate in producing feasible, high-quality convex transformations. This outperforms baseline methods by a significant margin, highlighting NC2C's ability to leverage LLMs for automated non-convex to convex transformation, reduce expert dependency, and enable efficient deployment of convex solvers for previously intractable optimization tasks.