一种混合的HS-FR共轭梯度算法

A mixed HS-FR conjugate gradient method

给出了一个混合的HS－FR共轭梯度算法，其中参数βk＝max｛0，min｝．在无充分下降性条件下，得到两个收敛性定理──定理3与定理4．其中定理3在下降条件与强Wolfe搜索准则下证明了梯度序列必有零聚点；定理4是定理3的改进，它表明在没有下降条件下定理3的结论仍然成立．

A mixed HS-FR conjugate gradient algorithm, in which parameter βk is chosen as βk= max { 0,min }, is proposed. Two convergence theorems without the sufficientdescent condition──theorem 3 and theorem 4, for the mixed HS-FR algorithm, are given.Theorem 3 proves that the sequence of generated gradients has a zero cluster under the descentcondition and the strong Wolfe search rule. Theorem 4 is an improvement of theorem3 which shows that the consequence of theorem 3 is still valid without the descent condition.