Exact finite-iteration convergence rates for DCA regimes $p_1$ through $p_4$

Let $f_1$ and $f_2$ have smoothness parameters $L_1,L_2$ and strong-convexity or hypoconvexity parameters $bc_1,bc_2$, and let $p_1,p_2,p_3,p_4$ denote the corresponding DCA parameter regimes. Let $N$ be the number of DCA iterations.

Finite-iteration tightness conjecture. The DCA rates corresponding to regimes $p_1$, $p_2$, $p_3$ and $p_4$ are tight for any number of iterations $N$.

These regimes include extensions of the standard difference-of-convex setting, while $p_3$ and $p_4$ arise beyond the threshold conditions separating the regimes. The source does not provide a proof and contrasts these cases with $p_5$ and $p_6$, whose rates are investigated only asymptotically.