| Fast projection onto the ordered weighted ℓ1 norm ball |
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| 作者姓名： | Qinzhen Li Xudong Li |
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| 作者单位： | School of Data Science;Shanghai Center for Mathematical Sciences |
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| 基金项目： | 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). |
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| 摘 要： | In this paper,we provide a finitely terminated yet efficient approach to compute the Euclidean projection onto the ordered weighted?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.
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| 关 键 词： | Euclidean projector ordered weighted?1norm ball HS-Jacobian semismooth Newton method |
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