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| Extrapolated Smoothing Descent Algorithm for Constrained Nonconvex and Nonsmooth Composite Problems* |
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Citation： |
Yunmei CHEN,Hongcheng LIU,Weina WANG.Extrapolated Smoothing Descent Algorithm for Constrained Nonconvex and Nonsmooth Composite Problems*[J].Chinese Annals of Mathematics B,2022,43(6):1049~1070 |
| Page view： 880
Net amount： 617 |
Authors： |
Yunmei CHEN; Hongcheng LIU;Weina WANG |
Foundation： |
National Natural Science Foundation of China (No. 12001144), Zhejiang Provincial Natural Science Foundation of China (No. LQ20A010007) and NSF/DMS-2152961. |
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| Abstract： |
In this paper, the authors propose a novel smoothing descent type algorithm with extrapolation for solving a class of constrained nonsmooth and nonconvex problems,where the nonconvex term is possibly nonsmooth. Their algorithm adopts the proximal gradient algorithm with extrapolation and a safe-guarding policy to minimize the smoothed objective function for better practical and theoretical performance. Moreover, the algorithm uses a easily checking rule to update the smoothing parameter to ensure that any accumulation point of the generated sequence is an (affine-scaled) Clarke stationary point of the original nonsmooth and nonconvex problem. Their experimental results indicate the effectiveness of the proposed algorithm. |
Keywords： |
Constrained nonconvex and nonsmooth optimization, Smooth approximation, Proximal gradient algorithm with extrapolation, Gradient descent algorithm, Image reconstruction |
Classification： |
94A08, 90C26 |
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