# NC2C: Automated Convexification of Generic Non-Convex Optimization Problems

arXiv: https://arxiv.org/abs/2601.04789 · HTML: https://mlsanity.com/paper/2601.04789/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 33 references that are in the map.
- First posted on arXiv 8 Jan 2026.

## Builds on (most cited first, 17 of 17)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [ToolLLM: Facilitating Large Language Models to Master 16000+ Real-world APIs](https://mlsanity.com/paper/2307.16789/) (2023)
- [Gorilla: Large Language Model Connected with Massive APIs](https://mlsanity.com/paper/2305.15334/) (2023)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Language Agent Tree Search Unifies Reasoning Acting and Planning in Language Models](https://mlsanity.com/paper/2310.04406/) (2023)
- [ToolRL: Reward is All Tool Learning Needs](https://mlsanity.com/paper/2504.13958/) (2025)
- [NL4Opt Competition: Formulating Optimization Problems Based on Their Natural Language Descriptions](https://mlsanity.com/paper/2303.08233/) (2023)
- [ToolChain*: Efficient Action Space Navigation in Large Language Models with A* Search](https://mlsanity.com/paper/2310.13227/) (2023)
- [LLMOPT: Learning to Define and Solve General Optimization Problems from Scratch](https://mlsanity.com/paper/2410.13213/) (2024)
- [OptiBench Meets ReSocratic: Measure and Improve LLMs for Optimization Modeling](https://mlsanity.com/paper/2407.09887/) (2024)
- [Seed-Prover 1.5: Mastering Undergraduate-Level Theorem Proving via Learning from Experience](https://mlsanity.com/paper/2512.17260/) (2025)
- [ToolEyes: Fine-Grained Evaluation for Tool Learning Capabilities of Large Language Models in Real-world Scenarios](https://mlsanity.com/paper/2401.00741/) (2024)
- [Tool-Planner: Task Planning with Clusters across Multiple Tools](https://mlsanity.com/paper/2406.03807/) (2024)
- [OptimAI: Optimization from Natural Language Using LLM-Powered AI Agents](https://mlsanity.com/paper/2504.16918/) (2025)

## Built on by (most cited first, 3 of 3)

- [Semantic Constraint Synthesis for Adaptive Trajectory Optimization via Large Language Models](https://mlsanity.com/paper/2606.04123/) (2026)
- [Constrained Path Reasoning: Measuring When Committed Stages Earn Their Cost](https://mlsanity.com/paper/2607.17240/) (2026)
- [Learning to Design Convex Relaxations for Nonconvex Optimization](https://mlsanity.com/paper/2610.16948/) (2026)

## Abstract (arXiv)

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.