一个修正HS共轭梯度法及其收敛性

A Modified Hestenes-Stiefel Conjugate Gradient Method and Its Convergence

中文关键词:  共轭梯度法  充分下降条件  线性搜索  全局收敛.

英文关键词:conjugate gradient method  sufficient descent condition  line search  global convergence.

中文摘要:

      众所周知,对于目标函数来说,由HS共轭梯度法产生的方向 不一定是下降方向.在这篇文章中,我们对HS共轭梯度法进行修正,由此产生的搜索方向总是满足充分下降条件.这个方法的一个优点是: $\beta_{k}^{HS*}$在弱Wolfe-Powell条件下保持非负.在适当的条件下,我们证明了该方法的全局收敛性.初步的数值结果表明:修正HS 方法比PRP和HS方法好一点.

英文摘要:

      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.