NC2C: Automated Convexification of Generic Non-Convex Optimization Problems

2026-01-08

arXiv.org

AI Summary

This work addresses the challenge of solving non-convex optimization problems, which are structurally complex and difficult for conventional solvers to handle efficiently, often requiring expert-guided manual convexification. To overcome this limitation, the authors propose NC2C, a novel framework that leverages large language models in an end-to-end manner to automatically convexify general non-convex problems. NC2C employs symbolic reasoning to identify non-convex components and integrates adaptive transformations, feasible region correction, and an iterative verification mechanism to generate equivalent convex formulations. Experimental results on a benchmark set of 100 general non-convex problems demonstrate that NC2C achieves an execution rate of 89.3% and a success rate of 76%, substantially outperforming existing baseline methods and significantly reducing reliance on human intervention.

Technology Category

• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Solvers and Tools
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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.

Problem

• non-convex optimization
• convexification
• automated transformation
• optimization solvers
• mathematical programming

Innovation

• automated convexification
• large language models
• non-convex optimization
• symbolic reasoning
• feasibility correction