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The cyclic Barzilai-Borwein method for unconstrained optimization

文献类型：期刊论文

作者Dai, Yu-Hong; Hager, William W.; Schittkowski, Klaus; Zhang, Hongchao
刊名IMA JOURNAL OF NUMERICAL ANALYSIS
出版日期2006-07-01
卷号26期号:3页码:604-627
关键词unconstrained optimization gradient method convex quadratic programming non-monotone line search
ISSN号0272-4979
DOI10.1093/imanum/dr1006
英文摘要In the cyclic Barzilai-Borwein (CBB) method, the same Barzilai-Borwein (BB) stepsize is reused for m consecutive iterations. It is proved that CBB is locally linearly convergent at a local minimizer with positive definite Hessian. Numerical evidence indicates that when m > n/2 >= 3, where n is the problem dimension, CBB is locally superlinearly convergent. In the special case m = 3 and n = 2, it is proved that the convergence rate is no better than linear, in general. An implementation of the CBB method, called adaptive cyclic Barzilai-Borwein (ACBB), combines a non-monotone line search and an adaptive choice for the cycle length m. In numerical experiments using the CUTEr test problem library, ACBB performs better than the existing BB gradient algorithm, while it is competitive with the well-known PRP+ conjugate gradient algorithm.
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000238907800009
出版者OXFORD UNIV PRESS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/3872]  
专题计算数学与科学工程计算研究所
通讯作者Dai, Yu-Hong
作者单位1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math & Sci Engn Comp, State Key Lab Sci & Engn Comp, Beijing 100084, Peoples R China
2.Univ Florida, Dept Math, Gainesville, FL 32611 USA
3.Univ Bayreuth, Dept Comp Sci, D-95440 Bayreuth, Germany
推荐引用方式
GB/T 7714		 Dai, Yu-Hong,Hager, William W.,Schittkowski, Klaus,et al. The cyclic Barzilai-Borwein method for unconstrained optimization[J]. IMA JOURNAL OF NUMERICAL ANALYSIS,2006,26(3):604-627.
APA Dai, Yu-Hong,Hager, William W.,Schittkowski, Klaus,&Zhang, Hongchao.(2006).The cyclic Barzilai-Borwein method for unconstrained optimization.IMA JOURNAL OF NUMERICAL ANALYSIS,26(3),604-627.
MLA Dai, Yu-Hong,et al."The cyclic Barzilai-Borwein method for unconstrained optimization".IMA JOURNAL OF NUMERICAL ANALYSIS 26.3(2006):604-627.

入库方式： OAI收割

来源：数学与系统科学研究院

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