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math.OC2026
Proximity Operator of the over Function
Lixin Shen, Guohui Song
We study the complete, possibly set-valued proximity operator of the nonconvex, scale-invariant ratio \(h(\vx)=\|\vx\|_{1}/\|\vx\|_{2}\). A polar decomposition of the nonzero branc…
math.OC2023
A Successive Two-stage Method for Sparse Generalized Eigenvalue Problems
Qia Li, Jianmin Liao, Lixin Shen +1
The Sparse Generalized Eigenvalue Problem (sGEP), a pervasive challenge in statistical learning methods including sparse principal component analysis, sparse Fisher's discriminant…
math.OC2015
A Simple Convergence Analysis of Bregman Proximal Gradient Algorithm
Yi Zhou, Yingbin Liang, Lixin Shen
In this paper, we provide a simple convergence analysis of proximal gradient algorithm with Bregman distance, which provides a tighter bound than existing result. In particular, fo…