NC2C: Automated Convexification of Generic Non-Convex Optimization Problems

ACL ARR 2026 January Submission5899 Authors

Keywords: Non-convex optimization, LLMs for Math, Instruction Learning

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 end-to-end automated framework designed to transform generic non-convex optimization problems into solvable convex forms. NC2C integrates symbolic reasoning, adaptive transformation techniques, and iterative validation to autonomously detect non-convex components, select optimal convexification strategies, and generate rigorous convex equivalents. Equipped with error correction loops and feasibility domain correction mechanisms, the framework ensures 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 streamline non-convex problem-solving, reduce expert dependency, and enable efficient deployment of convex solvers for previously intractable optimization tasks.

Paper Type: Long

Research Area: Mathematical, Symbolic, Neurosymbolic, and Logical Reasoning

Research Area Keywords: Mathematical reasoning, neural theorem provers, automatic evaluation

Contribution Types: Model analysis & interpretability, NLP engineering experiment, Reproduction study, Approaches to low-resource settings, Approaches low compute settings-efficiency, Publicly available software and/or pre-trained models, Data resources, Data analysis, Theory

Languages Studied: English

Submission Number: 5899