Global convergence of a modified Hestenes-Stiefel nonlinear conjugate gradient method with Armijo line search |
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Authors: | Zhifeng Dai Fenghua Wen |
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Institution: | (1) School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing, Wanzhou, People’s Republic of China |
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Abstract: | In this article, based on the modified secant equation, we propose a modified Hestenes-Stiefel (HS) conjugate gradient method
which has similar form as the CG-DESCENT method proposed by Hager and Zhang (SIAM J Optim 16:170–192, 2005). The presented method can generate sufficient descent directions without any line search. Under some mild conditions, we
show that it is globally convergent with Armijo line search. Moreover, the R-linear convergence rate of the modified HS method
is established. Preliminary numerical results show that the proposed method is promising, and competitive with the well-known
CG-DESCENT method. |
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Keywords: | |
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