Fast projection onto the ordered weighted ℓ_(1) norm ball  

作　　者：Qinzhen Li Xudong Li 

机构地区：[1]School of Data Science,Fudan University,Shanghai,200433,China [2]Shanghai Center for Mathematical Sciences,Fudan University,Shanghai,200433,China

出　　处：《Science China Mathematics》2022年第4期869-886,共18页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11901107);the Young Elite Scientists Sponsorship Program by CAST(Grant No.2019QNRC001);the Shanghai Sailing Program(Grant No.19YF1402600);the Science and Technology Commission of Shanghai Municipality Project(Grant No.19511120700).

摘　　要：In this paper,we provide a finitely terminated yet efficient approach to compute the Euclidean projection onto the ordered weightedℓ_(1)(OWL1)norm ball.In particular,an efficient semismooth Newton method is proposed for solving the dual of a reformulation of the original projection problem.Global and local quadratic convergence results,as well as the finite termination property,of the algorithm are proved.Numerical comparisons with the two best-known methods demonstrate the efficiency of our method.In addition,we derive the generalized Jacobian of the studied projector which,we believe,is crucial for the future designing of fast second-order nonsmooth methods for solving general OWL1 norm constrained problems.

关 键 词：Euclidean projector ordered weightedℓ_(1)norm ball HS-Jacobian semismooth Newton method 

分 类 号：O174[理学—数学]