Tolerance-aware certification for non-convex nonlinear models

Develop tighter tolerance-aware certificates for non-convex optimization models verified by SOVER’s dReal-based nonlinear extension.

Background

For nonlinear continuous reformulations, SOVER uses dReal’s δ-satisfiability and margin-separated queries to establish an ε-argmin guarantee rather than exact equivalence. The paper explicitly states that tighter tolerance-aware certificates remain important for non-convex models, where numerical tolerances and non-convexity can weaken the interpretation of verification results.

References

Several directions remain open. Improving LLM-based mapping synthesis could reduce inconclusive cases, while extending the verifier beyond bounded instances to dimension-parametric formulations would provide stronger guarantees for problem families. Although the dReal extension supports nonlinear continuous reformulations via $\delta$-satisfiability, tighter tolerance-aware certificates for non-convex models remain important.

— SOVER: Formal Certification of Optimization Reformulations via LLM-Assisted SMT Verification  (2609.00728 - Bhattacharyya et al., 1 Sep 2026) in Section 5, Conclusion and Future Work