NC2C: Automated Convexification of Generic Non-Convex Optimization Problems

TL;DR

NC2C tackles non-convex optimization by automating convexification through LLM reasoning, transforming each problem $\\mathcal{P}$ into a convex form $\\mathcal{P}_c$ via non-convex detection and strategy selection. It generates solver-ready code, executes it, and uses an Error Correction Loop (ECL) and Feasibility Domain Correction (FDC) to ensure feasibility relative to the original formulation, with solution validation guiding refinements. Across four diverse datasets, NC2C achieves high execution and success rates, outperforming several baselines and reducing reliance on expert knowledge for convexification. The approach demonstrates the potential of LLM-driven automated mathematical transformations to broaden access to convex solvers, while acknowledging dependencies on model reasoning and the added computational overhead of the multi-stage pipeline.

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.

Figures (5)

• Figure 1: Overview of the NC2C framework, which leverages LLMs to automatically transform generic non-convex optimization problems into convex forms.
• Figure 2: Impact of omitting key components of the NC2C framework on success and execution rates across GPT-5.1 and Qwen3-235B-A22B.
• Figure 3: Success and execution rates for NC2C under different maximum iteration counts for ECL and FDC.
• Figure 4: Average Running Time of NC2C and Baseline Methods on GPT-5.1 and Qwen3-235B.
• Figure 5: Pie chart of the time proportion of each part.