10.6084/m9.figshare.5503729.v1
Tzu-Ying Liu
Hui Jiang
Minimizing Sum of Truncated Convex Functions and Its Applications
2017
Taylor & Francis Group
ℓ0 penalty
Non-convex optimization
NP-Hard
Outlier detection
signal and image restoration
2017-10-16 18:48:02
article
https://tandf.figshare.com/articles/Minimizing_Sum_of_Truncated_Convex_Functions_and_Its_Applications/5503729
<p>In this article, we study a class of problems where the sum of truncated convex functions is minimized. In statistical applications, they are commonly encountered when ℓ<sub>0</sub>-penalized models are fitted and usually lead to NP-Hard non-convex optimization problems. In this article, we propose a general algorithm for the global minimizer in low-dimensional settings. We also extend the algorithm to high-dimensional settings, where an approximate solution can be found efficiently. We introduce several applications where the sum of truncated convex functions is used, compare our proposed algorithm with other existing algorithms in simulation studies, and show its utility in edge-preserving image restoration on real data.</p>