Extrapolated Smoothing Descent Algorithm for Constrained Nonconvex and Nonsmooth Composite Problems
Extrapolated Smoothing Descent Algorithm for Constrained Nonconvex and Nonsmooth Composite Problems
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DOI：
10.1007/s11401-022-0377-7
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发表时间：
2022-11
期刊：
影响因子：
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通讯作者：
Yunmei Chen;Hongcheng Liu;Weina Wang
中科院分区：
文献类型：
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作者：
Yunmei Chen;Hongcheng Liu;Weina Wang
针对一类约束非光滑非凸问题，提出了一种新的带外推的光滑下降型算法，其中非凸项可能是非光滑的。该算法采用了带有外推的近似梯度算法和一种安全保护策略，以最小化平滑后的目标函数，从而获得更好的实际和理论性能。此外，该算法使用一个易于检查的规则来更新平滑参数，以确保生成序列的任何聚点都是原非光滑非凸问题的（仿射尺度）Clarke平稳点.实验结果表明了该算法的有效性。
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.