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.

翻译：非凸优化问题在数学规划、工程设计和科学计算中普遍存在，由于其复杂的目标函数和约束条件，往往给传统求解器带来难以处理的挑战。为解决人工凸化效率低下及过度依赖专家知识的问题，我们提出了NC2C——一种基于大语言模型的端到端自动化框架，旨在利用大语言模型将通用非凸优化问题转化为可求解的凸形式。NC2C借助大语言模型的数学推理能力，自主检测非凸成分、选择最优凸化策略，并生成严格的凸等价形式。该框架集成了符号推理、自适应转换技术和迭代验证机制，配备误差校正循环与可行域修正模块，以确保转换后问题的鲁棒性与有效性。在包含100个通用非凸问题的多样化数据集上的实验结果表明，NC2C实现了89.3%的执行率与76%的成功率，能够生成可行且高质量的凸转换形式。其性能显著优于基线方法，凸显了NC2C利用大语言模型实现非凸到凸的自动转换、降低专家依赖性，并为以往难以处理的优化任务高效部署凸求解器的能力。