数学季刊 ›› 2023, Vol. 38 ›› Issue (1): 62-84.doi: 10.13371/j.cnki.chin.q.j.m.2023.01.005
收稿日期:
2022-04-14
出版日期:
2023-03-30
发布日期:
2023-03-20
通讯作者:
JIN Ling-Zi (1997-), female, native of Chun’an, Zhejiang, master student of University of Chinese
Academy of Sciences, engages in operations research and cybernetics.
E-mail:jinlingzi19@mails.ucas.ac.cn
作者简介:
JIN Ling-Zi (1997-), female, native of Chun’an, Zhejiang, master student of University of Chinese
Academy of Sciences, engages in operations research and cybernetics.
基金资助:
Received:
2022-04-14
Online:
2023-03-30
Published:
2023-03-20
Contact:
JIN Ling-Zi (1997-), female, native of Chun’an, Zhejiang, master student of University of Chinese
Academy of Sciences, engages in operations research and cybernetics.
E-mail:jinlingzi19@mails.ucas.ac.cn
About author:
JIN Ling-Zi (1997-), female, native of Chun’an, Zhejiang, master student of University of Chinese
Academy of Sciences, engages in operations research and cybernetics.
Supported by:
摘要: This paper studies a class of nonconvex composite optimization, whose
objective is a summation of an average of nonconvex (weakly) smooth functions and a
convex nonsmooth function, where the gradient of the former function has the Hölder
continuity. By exploring the structure of such kind of problems, we first propose a
proximal (quasi-)Newton algorithm wPQN (Proximal quasi-Newton algorithm for weakly
smooth optimization) and investigate its theoretical complexities to find an approximate
solution. Then we propose a stochastic variant algorithm wPSQN (Proximal stochastic
quasi-Newton algorithm for weakly smooth optimization), which allows a random subset
of component functions to be used at each iteration. Moreover, motivated by recent
success of variance reduction techniques, we propose two variance reduced algorithms,
wPSQN-SVRG and wPSQN-SARAH, and investigate their computational complexity
separately.
中图分类号:
金玲子. 一类非凸优化问题的邻近拟牛顿方法的复杂性[J]. 数学季刊, 2023, 38(1): 62-84.
JIN Ling-Zi . Complexity on Proximal Quasi-Newton Methods for a Class of Nonconvex Composite Optimization[J]. Chinese Quarterly Journal of Mathematics, 2023, 38(1): 62-84.
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