Extrapolated Smoothing Descent Algorithm for Constrained Nonconvex and Nonsmooth Composite Problems

Yunmei CHEN; Hongcheng LIU; Weina WANG

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Extrapolated Smoothing Descent Algorithm for Constrained Nonconvex and Nonsmooth Composite Problems

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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(afne-scaled)Clarke stationary point of the original nonsmooth and nonconvex problem.Their experimental results indicate the effectiveness of the proposed algorithm.

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《数学年刊B辑（英文版）》 |2022年第6期|1049-1070|共22页
作者
Yunmei CHEN; Hongcheng LIU; Weina WANG;
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作者单位

Department of Mathematics;

University of Florida;

Gainesville 118105;

USA;

Industrial and Systems Engineering;

University of Florida;

Gainesville 118105;

USA;

Corresponding author.Department of Mathematics;

Hangzhou Dianzi University;

Hangzhou 310018;

China;

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原文格式 PDF
正文语种 chi
中图分类最优化的数学理论;
关键词
Constrained nonconvex and nonsmooth optimization; Smooth approximation; Proximal gradient algorithm with extrapolation; Gradient descent algorithm; Image reconstruction;

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Extrapolated Smoothing Descent Algorithm for Constrained Nonconvex and Nonsmooth Composite Problems

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