Abstract
In this paper, by minimizing the distance between the CG direction and the direction of the improved Perry conjugate gradient method [Yao et al., Numer. Algorithms 78 (2018) 1255–1269], we propose a descent modified HS conjugate gradient method. A remarkable property of the modified HS method is that it can produce sufficient descent property, which is independent of the line search used. Under suitable conditions, we prove that the modified HS method with the standard Armijo line search is globally convergent for uniformly convex functions and the modified HS+ method with standard Wolfe line search is globally convergent for general nonlinear functions. Extensive numerical experiments show that the proposed method is efficient.
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