Extrapolated Smoothing Descent Algorithm for Constrained Nonconvex and Nonsmooth Composite Problems

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-gua...

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Vydané v:Chinese annals of mathematics. Serie B Ročník 43; číslo 6; s. 1049 - 1070
Hlavní autori: Chen, Yunmei, Liu, Hongcheng, Wang, Weina
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2022
Springer Nature B.V
Department of Mathematics,University of Florida,Gainesville 118105,USA%Industrial and Systems Engineering,University of Florida,Gainesville 118105,USA%Department of Mathematics,Hangzhou Dianzi University,Hangzhou 310018,China
Predmet:
Algorithms
Applications of Mathematics
Extrapolation
Mathematics
Mathematics and Statistics
Smoothing
Smooth approximation
65K05
65F22
94A08
Gradient descent algorithm
90C26
Proximal gradient algorithm with extrapolation
Image reconstruction
Constrained nonconvex and nonsmooth optimization
Smooth approxi-mation
Gradient de-scent algorithm
ISSN:0252-9599, 1860-6261
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Shrnutí: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.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0252-9599
1860-6261
DOI:10.1007/s11401-022-0377-7