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In this paper, we study a class of problems where the sum of truncated convexfunctions is minimized. In statistical applications, they are commonlyencountered when $\ell_0$-penalized models are fitted and usually lead toNP-Hard non-convex optimization problems. In this paper, we propose a generalalgorithm for the global minimizer in low-dimensional settings. We also extendthe algorithm to high-dimensional settings, where an approximate solution canbe found efficiently. We introduce several applications where the sum oftruncated convex functions is used, compare our proposed algorithm with otherexisting algorithms in simulation studies, and show its utility inedge-preserving image restoration on real data.

Minimizing Sum of Truncated Convex Functions and Its Applications