arXiv Machine Learning August 20, 2026 By Ali Hussaini Umar, Jean Barbier, Matthieu Jonckheere, Manuel S\'aenz

On the Slow Convergence to Trivial Solutions of Algorithms for Hard Optimization Problems

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The paper investigates how optimization algorithms for hard combinatorial problems converge to trivial solutions. By combining rigorous large‑graph asymptotics with numerical experiments on maximum independent set and maximum K‑SAT, the authors show that convergence to the theoretically predicted bounds is extremely slow, especially in the intermediate regime of high constraint density. This reveals a significant gap between finite‑size performance and asymptotic expectations, indicating that practical algorithm design remains essential even when theory predicts inevitable failure.

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