  Recently, the anchor acceleration, an acceleration mechanism distinct from
Nesterov's, has been discovered for minimax optimization and fixed-point
problems, but its mechanism is not understood well, much less so than Nesterov
acceleration. In this work, we analyze continuous-time models of anchor
acceleration. We provide tight, unified analyses for characterizing the
convergence rate as a function of the anchor coefficient $\beta(t)$, thereby
providing insight into the anchor acceleration mechanism and its accelerated
$\mathcal{O}(1/k^2)$-convergence rate. Finally, we present an adaptive method
inspired by the continuous-time analyses and establish its effectiveness
through theoretical analyses and experiments.
