For the fast iterative shrinkage algorithm, the authors write
Can someone explain why this algorithm is for constant step-size, when the step-size $t_k$ is obviously dynamically varying?
2026-03-26 01:09:43.1774487383
Why do we update step-size for constant step-size FISTA?
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$t_k$ is not the step-size. It's an internal parameter of the algorithm, which does not depend on the functions $f$ and $g$ which make up the objective. In many cases it is called the momentum factor.
The step size is $\frac{1}{L}$, and it is indeed constant. You can see that in every iteration the $L$ is the same (step 4.1). See the definition of $p_L$ in the paper.