Structured Sparsity Promoting Functions

Lixin Shen (), Bruce W. Suter () and Erin E. Tripp ()
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Lixin Shen: Syracuse University
Bruce W. Suter: Air Force Research Laboratory
Erin E. Tripp: Syracuse University

Journal of Optimization Theory and Applications, 2019, vol. 183, issue 2, No 2, 386-421

Abstract: Abstract Motivated by the minimax concave penalty-based variable selection in high-dimensional linear regression, we introduce a simple scheme to construct structured sparsity promoting functions from convex sparsity promoting functions and their Moreau envelopes. Properties of these functions are developed by leveraging their structure. In particular, we provide sparsity guarantees for the general family of functions. We further study the behavior of the proximity operators of several special functions, including indicator functions of closed and convex sets, piecewise quadratic functions, and linear combinations of the two. To demonstrate these properties, several concrete examples are presented and existing instances are featured as special cases.

Keywords: Moreau envelope; Proximity operator; Variable selection; Sparsity; Thresholding operator; 90C26; 90C30; 65K99 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10957-019-01565-0

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