CONVERGENCE RATE OF GRADIENT DESCENT METHOD FOR MULTI-OBJECTIVE OPTIMIZATION

doi:10.4208/jcm.1808-m2017-0214

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	CONVERGENCE RATE OF GRADIENT DESCENT METHOD FOR MULTI-OBJECTIVE OPTIMIZATION
	Zeng, Liaoyuan 1; Dai, Yuhong 1; Huang, Yakui 2
	2019
发表期刊	JOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN	0254-9409
卷号	37 期号:5 页码:689-703
摘要	The convergence rate of the gradient descent method is considered for unconstrained multi-objective optimization problems (MOP). Under standard assumptions, we prove that the gradient descent method with constant stepsizes converges sublinearly when the objective functions are convex and the convergence rate can be strengthened to be linear if the objective functions are strongly convex. The results are also extended to the gradient descent method with the Armijo line search. Hence, we see that the gradient descent method for MOP enjoys the same convergence properties as those for scalar optimization.
关键词	Multi-objective optimization Gradient descent Convergence rate
DOI	10.4208/jcm.1808-m2017-0214
收录类别	SCI
语种	英语
资助项目	Chinese Natural Science Foundation[11631013] ; Chinese Natural Science Foundation[11971372] ; National 973 Program of China[2015CB856002]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000504737600006
出版者	GLOBAL SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/50443
专题	中国科学院数学与系统科学研究院
通讯作者	Dai, Yuhong
作者单位	1.Chinese Acad Sci, State Key Lab Sci & Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Hebei Univ Technol, Sch Sci, Tianjin 300401, Peoples R China
推荐引用方式 GB/T 7714	Zeng, Liaoyuan,Dai, Yuhong,Huang, Yakui. CONVERGENCE RATE OF GRADIENT DESCENT METHOD FOR MULTI-OBJECTIVE OPTIMIZATION[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,2019,37(5):689-703.
APA	Zeng, Liaoyuan,Dai, Yuhong,&Huang, Yakui.(2019).CONVERGENCE RATE OF GRADIENT DESCENT METHOD FOR MULTI-OBJECTIVE OPTIMIZATION.JOURNAL OF COMPUTATIONAL MATHEMATICS,37(5),689-703.
MLA	Zeng, Liaoyuan,et al."CONVERGENCE RATE OF GRADIENT DESCENT METHOD FOR MULTI-OBJECTIVE OPTIMIZATION".JOURNAL OF COMPUTATIONAL MATHEMATICS 37.5(2019):689-703.