一个修正HS共轭梯度法及其收敛性

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 βkH Sffikeeps 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.

A Modified Hestenes-Stiefel Conjugate Gradient Method and Its Convergence

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.