A unified high-resolution ODE framework for first-order methods

Lixia Wang, Hao Luo

For a generic discrete-time algorithm (DTA): $z^{+}=g(z,s)$, where $s$ is the step size, Lu (Math. Program., 194(1):1061--1112, 2022) proposed an $O(s^r)$-resolution ordinary differe…