Farkas Dual Rays Do Not Improve LLM-Based Optimization Model Repair

Abstract

Large language models (LLMs) can translate natural language optimization problems into mathematical formulations, but frequently generate infeasible models. We investigate whether Farkas dual ray multipliers---which provide a certificate of infeasibility with constraint-level contributions---can improve LLM-based repair by ranking which constraints to show when the Irreducible Infeasible Subsystem (IIS) must be truncated. We propose DualRayRank, which ranks IIS constraints by their Farkas multiplier magnitudes and provides the top-$K$ to the LLM. In controlled experiments on MAMO-Optimization, we find that DualRayRank produces identical results to baseline IIS-TopK: both achieve 1/31 (3.23%) repair rate under matched conditions, repairing the same instance. The truncation regime where ranking could theoretically help shows 0/16 repair success. Furthermore, simple Best-of-2 inference scaling (65.12% Pass@1) outperforms all repair methods including optimized configurations with 10$\times$ larger models (58.86%). We report this negative result to guide future research away from feedback-format optimization toward more fundamental improvements.