Affiliation:
1. School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510520, P. R. China
Abstract
Computing the proximal operator of the sparsity-promoting piece-wise exponential (PiE) penalty [Formula: see text] with a given shape parameter [Formula: see text], which is treated as a popular nonconvex surrogate of [Formula: see text]-norm, is fundamental in feature selection via support vector machines, image reconstruction, zero-one programming problems, compressed sensing, neural networks, etc. Due to the nonconvexity of PiE, for a long time, its proximal operator is frequently evaluated via an iteratively reweighted [Formula: see text] algorithm, which substitutes PiE with its first-order approximation, however, the obtained solutions only are the critical point. Based on the exact characterization of the proximal operator of PiE, we explore how the iteratively reweighted [Formula: see text] solution deviates from the true proximal operator in certain regions, which can be explicitly identified in terms of [Formula: see text], the initial value and the regularization parameter in the definition of the proximal operator. Moreover, the initial value can be adaptively and simply chosen to ensure that the iteratively reweighted [Formula: see text] solution belongs to the proximal operator of PiE.
Funder
National Natural Science Foundation of China
Science and Technology Program of Guangzhou
Opening Project of Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University
Guangdong Basic and Applied Basic Research Foundation
Publisher
World Scientific Pub Co Pte Ltd