Yihan Cang

Xinyue Peng, Yanming Liu, Yihan Cang et al.

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.

Xinyue Peng, Yanming Liu, Yihan Cang et al.

Solving non-convex resource allocation problems poses significant challenges in wireless communication systems, often beyond the capability of traditional optimization techniques. To address this issue, we propose LLM-OptiRA, the first framework that leverages large language models (LLMs) to automatically detect and transform non-convex components into solvable forms, enabling fully automated resolution of non-convex resource allocation problems in wireless communication systems. LLM-OptiRA not only simplifies problem-solving by reducing reliance on expert knowledge, but also integrates error correction and feasibility validation mechanisms to ensure robustness. Experimental results show that LLM-OptiRA achieves an execution rate of 96% and a success rate of 80% on GPT-4, significantly outperforming baseline approaches in complex optimization tasks across diverse scenarios.