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On restart procedures for the conjugate gradient method
Dai, YH; Liao, LZ; Li, D
AbstractThe conjugate gradient method is a powerful solution scheme for solving unconstrained optimization problems, especially for large-scale problems. However, the convergence rate of the method without restart is only linear. In this paper, we will consider an idea contained in [16] and present a new restart technique for this method. Given an arbitrary descent direction d(t) and the gradient g(t), our key idea is to make use of the BFGS updating formula to provide a symmetric positive definite matrix P-t such that d(t) = - P-t g(t) , and then define the conjugate gradient iteration in the transformed space. Two conjugate gradient algorithms are designed based on the new restart technique. Their global convergence is proved under mild assumptions on the objective function. Numerical experiments are also reported, which show that the two algorithms are comparable to the Beale-Powell restart algorithm.
Keywordunconstrained optimization conjugate gradient method BFGS updating formula restart global convergence
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000220453200008
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Document Type期刊论文
Corresponding AuthorDai, YH
Affiliation1.Chinese Acad Sci, State Key Lab Sci & Engn Comp, Inst Computat Math & Sci Engn Comp, Beijing 100080, Peoples R China
2.Hong Kong Baptist Univ, Dept Math, Kowloon, Hong Kong, Peoples R China
3.Chinese Univ Hong Kong, Dept Syst Engn & Engn Management, Shatin, Hong Kong, Peoples R China
Recommended Citation
GB/T 7714
Dai, YH,Liao, LZ,Li, D. On restart procedures for the conjugate gradient method[J]. NUMERICAL ALGORITHMS,2004,35(2-4):249-260.
APA Dai, YH,Liao, LZ,&Li, D.(2004).On restart procedures for the conjugate gradient method.NUMERICAL ALGORITHMS,35(2-4),249-260.
MLA Dai, YH,et al."On restart procedures for the conjugate gradient method".NUMERICAL ALGORITHMS 35.2-4(2004):249-260.
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