Higher-order optimization methods can solve monotone inclusion problems with complexity O(ε^{-2/(3p-1)}), which is provably optimal and improves prior bounds by using anchored extrapolation with Taylor approximations of operators.
This paper develops optimal higher-order methods for solving monotone inclusion problems—a fundamental class of optimization problems. The authors introduce the Anchored Extra-Proximal framework that achieves better convergence rates than prior methods by combining extrapolation with proximal updates. They prove their approach is optimal up to logarithmic factors across all orders.