A descent modified HS conjugate gradient method with an optimal property

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