SOVER: Formal Certification of Optimization Reformulations via LLM-Assisted SMT Verification
Year: 2026
Type: conference-paper
Abstract: Large Language Models (LLMs) have shown remarkable promise in translating and reformulating complex mathematical optimization problems across modeling languages.However, validating such transformations through empirical solver executions alone is unreliable, as solver outcomes may be affected by local minima, structural timeouts, numerical artifacts, and subtle semantic divergence between formulations.We introduce SOVER, an LLM-assisted SMT framework that separates semantic mapping from formal certification: Z3 checks domain cross-feasibility and global objectiveorder preservation for mixed-integer linear formulations, while dReal provides toleranceaware feasibility/range and ϵ-argmin checks for continuous nonlinear formulations.We also introduce NLEQUIV-150, a public benchmark of 100 equivalent and 50 deliberately hard non-equivalent nonlinear reformulation pairs.With LLM-extracted mappings, SOVER classifies 149/150 pairs (99.33%) correctly, including all 50 hard negatives; the sole error is an incomplete mapping extraction.
Authors: Swapnil Bhattacharyya, Mayank Baranwal
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W7206214964