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CONVERGENCE RATE OF GRADIENT DESCENT METHOD FOR MULTI-OBJECTIVE OPTIMIZATION
Zeng, Liaoyuan1; Dai, Yuhong1; Huang, Yakui2
2019
Source PublicationJOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN0254-9409
Volume37Issue:5Pages:689-703
AbstractThe 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.
KeywordMulti-objective optimization Gradient descent Convergence rate
DOI10.4208/jcm.1808-m2017-0214
Indexed BySCI
Language英语
Funding ProjectChinese Natural Science Foundation[11631013] ; Chinese Natural Science Foundation[11971372] ; National 973 Program of China[2015CB856002]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000504737600006
PublisherGLOBAL SCIENCE PRESS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/50443
Collection中国科学院数学与系统科学研究院
Corresponding AuthorDai, Yuhong
Affiliation1.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
Recommended Citation
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.
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