An efficient Lagrangian smoothing heuristic for Max-Cut

Max-Cut is a famous NP-hard problem in combinatorial optimization. In this article, we propose a Lagrangian smoothing algorithm for Max-Cut, where the continuation subproblems are solved by the truncated Frank-Wolfe algorithm. We establish practical stopping criteria and prove that our algorithm finitely terminates at a KKT point, the distance between which and the neighbour optimal solution is also estimated. Additionally, we obtain a new sufficient optimality condition for Max-Cut. Numerical results indicate that our approach outperforms the existing smoothing algorithm in less time.