Change-point problems have appeared in a great many applications for example cancer genetics, econometrics and climate change. Modern multiscale type segmentation methods are considered to be a statistically efficient approach for multiple change-point detection, which minimize the number of change-points under a multiscale side-constraint. The constraint threshold plays a critical role in balancing the data-fit and model complexity. However, the computation time of such a threshold is quadratic in terms of sample size $n$, making it impractical for large scale problems. In this paper we proposed an $\mathcal{O}(n)$ algorithm by utilizing the hidden quasiconvexity structure of the problem. It applies to all regression models in exponential family with arbitrary convex scale penalties. Simulations verify its computational efficiency and accuracy. An implementation is provided in R-package "linearQ" on CRAN.