Chambolle-Pock converges weakly to a KKT point for 0 < θ ≤ 1 when τσ‖L‖² is below 4θ(2-θ)/(1-2θ+9θ²-4θ³), with ergodic duality gap O(1/k).
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The Chambolle-Pock method also converges weakly with $0 < \theta \le 1$ and $\tau\sigma\|L\|^{2} < 4\theta(2-\theta)/(1 - 2\theta + 9\theta^{2} - 4\theta^{3})$
Chambolle-Pock converges weakly to a KKT point for 0 < θ ≤ 1 when τσ‖L‖² is below 4θ(2-θ)/(1-2θ+9θ²-4θ³), with ergodic duality gap O(1/k).