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A family of spectral gradient methods for optimization
Dai, Yu-Hong1,2; Huang, Yakui3; Liu, Xin-Wei3
AbstractWe propose a family of spectral gradient methods, whose stepsize is determined by a convex combination of the long Barzilai-Borwein (BB) stepsize and the short BB stepsize. Each member of the family is shown to share certain quasi-Newton property in the sense of least squares. The family also includes some other gradient methods as its special cases. We prove that the family of methods is R-superlinearly convergent for two-dimensional strictly convex quadratics. Moreover, the family is R-linearly convergent in the any-dimensional case. Numerical results of the family with different settings are presented, which demonstrate that the proposed family is promising.
KeywordUnconstrained optimization Steepest descent method Spectral gradient method R-linear convergence R-superlinear convergence
Funding ProjectNational Natural Science Foundation of China[11631013] ; National Natural Science Foundation of China[11701137] ; National Natural Science Foundation of China[11671116] ; National 973 Program of China[2015CB856002]
WOS Research AreaOperations Research & Management Science ; Mathematics
WOS SubjectOperations Research & Management Science ; Mathematics, Applied
WOS IDWOS:000476600200002
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Document Type期刊论文
Corresponding AuthorHuang, Yakui
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Math Sci, Beijing 100049, Peoples R China
3.Hebei Univ Technol, Inst Math, Tianjin 300401, Peoples R China
Recommended Citation
GB/T 7714
Dai, Yu-Hong,Huang, Yakui,Liu, Xin-Wei. A family of spectral gradient methods for optimization[J]. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,2019,74(1):43-65.
APA Dai, Yu-Hong,Huang, Yakui,&Liu, Xin-Wei.(2019).A family of spectral gradient methods for optimization.COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,74(1),43-65.
MLA Dai, Yu-Hong,et al."A family of spectral gradient methods for optimization".COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 74.1(2019):43-65.
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