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 meth...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 βκHS. 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.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No.10761001)
文摘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 βκHS. 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.
