AI-Assisted Discovery of Convex Relaxations via Dual Agents

arXiv:2606.31182v1 Announce Type: new Abstract: Recent work shows that LLM agents can improve sharp-constant inequalities by searching for extremal constructions, which yield upper bounds. We address the complementary side: a lower bound holds for every admissible function and follows from a convex relaxation of the nonconvex problem, with tighter relaxations giving stronger bounds. We instantiate the autoresearch paradigm to discover such relaxations: a coding agent proposes valid tightening constraints, a theory agent verifies each one and searches for counterexamples, and every reported bound is certified by an explicit dual-feasible point checked in rigorous interval arithmetic. On two optimization constants studied by itet{tao2025alphaevolve} - the first autocorrelation inequality (C_{6.2}) and the Erdos minimum-overlap constant (C_{6.5}) - we improve the certified lower bounds from 1.28 to 1.2937 and from 0.379005 to 0.37912, respectively.

Source: arXiv cs.AI | 2026-07-01