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Convergence properties of the BFGS algoritm
Dai, YH
AbstractThe BFGS method is one of the most famous quasi-Newton algorithms for unconstrained optimization. In 1984, Powell presented an example of a function of two variables that shows that the Polak-Ribiere-Polyak (PRP) conjugate gradient method and the BFGS quasi-Newton method may cycle around eight nonstationary points if each line search picks a local minimum that provides a reduction in the objective function. In this paper, a new technique of choosing parameters is introduced, and an example with only six cyclic points is provided. It is also noted through the examples that the BFGS method with Wolfe line searches need not converge for nonconvex objective functions.
Keywordunconstrained optimization conjugate gradient method quasi-Newton method Wolfe line search nonconvex global convergence
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000181475800004
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Document Type期刊论文
Corresponding AuthorDai, YH
AffiliationChinese Acad Sci, Acad Math & Syst Sci, Inst Computat Mach & Sci Engn Comp, State Key Lab Sci & Engn Comp, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Dai, YH. Convergence properties of the BFGS algoritm[J]. SIAM JOURNAL ON OPTIMIZATION,2003,13(3):693-701.
APA Dai, YH.(2003).Convergence properties of the BFGS algoritm.SIAM JOURNAL ON OPTIMIZATION,13(3),693-701.
MLA Dai, YH."Convergence properties of the BFGS algoritm".SIAM JOURNAL ON OPTIMIZATION 13.3(2003):693-701.
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