AI Agents Discover Tighter Convex Relaxations for Optimization Problems.

Researchers have developed an AI-driven approach to enhance the discovery of convex relaxations, which are crucial for finding lower bounds in non-convex optimization problems. This new paradigm employs a system of "dual agents": a coding agent proposes potential tightening constraints, while a theory agent rigorously verifies these proposals and searches for counterexamples. All discovered bounds are then certified using explicit dual-feasible points, checked with interval arithmetic for mathematical rigor. The method was applied to two specific optimization constants, the first autocorrelation inequality ($C_{6.2}$) and the Erdős minimum-overlap constant ($C_{6.5}$). The AI system successfully improved the certified lower bounds for both, moving from 1.28 to 1.2937 for the former and from 0.379005 to 0.37912 for the latter. This demonstrates the potential of AI agents to push the boundaries of mathematical discovery and optimization.