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The cyclic Barzilai-Borwein method for unconstrained optimization
Dai, Yu-Hong; Hager, William W.; Schittkowski, Klaus; Zhang, Hongchao
AbstractIn 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.
Keywordunconstrained optimization gradient method convex quadratic programming non-monotone line search
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000238907800009
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Document Type期刊论文
Corresponding AuthorDai, Yu-Hong
Affiliation1.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
Recommended Citation
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.
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