Definition. Effective optimizer clock [ftip-00BM]
Definition. Effective optimizer clock [ftip-00BM]
For the flow of Definition [ftip-00BL], define the effective optimizer clock
\[ \tau (t)=\int _0^t\frac {du}{a(u)}, \qquad \tau _{\max }=\int _0^\infty \frac {du}{a(u)}, \qquad 0<\tau _{\max }\leq \infty . \]The clock is strictly increasing on its domain. If \(\tau _{\max }=\infty \), it reaches every gradient-flow time; otherwise it traverses only the prefix with effective time below \(\tau _{\max }\).