A Modified Hestenes-Stiefel Conjugate Gradient Method and Its Convergence
Received:December 22, 2007  Revised:May 21, 2008
Key Word: conjugate gradient method   sufficient descent condition   line search   global convergence.  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.10761001).
Author NameAffiliation
Zeng Xin WEI College of Mathematics and Information Science, Guangxi University, Guangxi 530004, P. R. China 
Hai Dong HUANG College of Mathematics and Information Science, Guangxi University, Guangxi 530004, P. R. China 
Yan Rong TAO College of Mathematics and Information Science, Guangxi University, Guangxi 530004, P. R. China 
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Abstract:
      It is well-known that the direction generated by Hestenes-Stiefel (HS) conjugate gradient method may not be a descent direction for the objective function. In this paper, we take a little modification to the HS method, then the generated direction always satisfies the sufficient descent condition. An advantage of the modified Hestenes-Stiefel (MHS) method is that the scalar $\beta_{k}^{HS*}$ keeps nonnegative under the weak Wolfe-Powell line search. The global convergence result of the MHS method is established under some mild conditions. Preliminary numerical results show that the MHS method is a little more efficient than PRP and HS methods.
Citation:
DOI:10.3770/j.issn:1000-341X.2010.02.013
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