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Alternate step gradient method
Dai, YH
2003-08-01
Source PublicationOPTIMIZATION
ISSN0233-1934
Volume52Issue:4-5Pages:395-415
AbstractThe Barzilai and Borwein (BB) gradient method does not guarantee a descent in the objective function at each iteration, but performs better than the classical steepest descent (SD) method in practice. So far, the BB method has found many successful applications and generalizations in linear systems. unconstrained optimization, convex-constrained optimization, stochastic optimization, etc. In this article. we propose a new gradient method that uses the SD and the 1313 steps alternately. Hence the name "alternate step (AS) gradient method." Our theoretical and numerical analyses show that the AS method is a promising alternative to the 1313 method for linear systems. Unconstrained optimization algorithms related to the AS method are also discussed. particularly, a more efficient gradient algorithm is provided by exploring the idea of the AS method in the GBB algorithm by Raydan (1997). To establish a general R-linear convergence result for gradient methods, an important property of the stepsize is drawn in this article. Consequently, R-linear convergence result is established for a large collection of gradient methods, including the AS method. Some interesting insights into gradient methods and discussion about monotonicity and nonmonotonicity are also given.
Keywordlinear system unconstrained optimizations gradient method convergence rate nonmonotone line search
DOI10.1080/02331930310001611547
Language英语
WOS Research AreaOperations Research & Management Science ; Mathematics
WOS SubjectOperations Research & Management Science ; Mathematics, Applied
WOS IDWOS:000186897600003
PublisherTAYLOR & FRANCIS LTD
Citation statistics
Cited Times:39[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/18738
Collection中国科学院数学与系统科学研究院
AffiliationChinese Acad Sci, State Key Lab Sci & Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Dai, YH. Alternate step gradient method[J]. OPTIMIZATION,2003,52(4-5):395-415.
APA Dai, YH.(2003).Alternate step gradient method.OPTIMIZATION,52(4-5),395-415.
MLA Dai, YH."Alternate step gradient method".OPTIMIZATION 52.4-5(2003):395-415.
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