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Global convergence of a modified Hestenes-Stiefel nonlinear conjugate gradient method with Armijo line search. (English) Zbl 1238.65052
Based on the modified secant equation, the authors propose a modified Hestenes-Stiefel (HS) conjugate gradient method that has similar form as the CG-DESCENT method proposed by {\it W. W. Hager} and {\it H. Zhang} [SIAM J. Optim. 16, No. 1, 170--192 (2005; Zbl 1093.90085)]. The presented method can generate sufficient descent directions without any line search. Under some mild conditions, it is shown that the new method 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.

65K05Mathematical programming (numerical methods)
90C30Nonlinear programming
Full Text: DOI
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