A globally convergent version of the Polak-Ribiere conjugate gradient method
A globally convergent version of the Polak-Ribiere conjugate gradient method
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DOI：
10.1007/bf02614362
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发表时间：
1997-09-01
影响因子：
2.7
通讯作者：
Lucidi, S
中科院分区：
文献类型：
--
作者：
Grippo, L;Lucidi, S
在本文中，我们提出了一个新的线搜索算法，确保全局收敛的Polak-Ribiere共轭梯度法的无约束最小化的非凸可微函数。特别是，我们表明，与此线搜索的Polak-Ribiere迭代产生的每一个极限点是一个固定点的目标函数。此外，我们定义了自适应规则的参数选择的方式，沿沿着搜索方向的第一个静止点，可以最终接受的算法收敛到一个最小值点正定Hessian矩阵。在强凸性假设下，作为一种特殊情况，重新得到了已知的全局收敛性结果。从计算的角度来看，我们可以预期，一个算法，将步长接受规则提出这里将保留相同的好功能的Polak-Ribiere方法，同时避免病理情况。(C)1997年，数学编程学会（Mathematical Programming Society，Inc.）出版社：Elsevier Science B. V.
In this paper we propose a new line search algorithm that ensures global convergence of the Polak-Ribiere conjugate gradient method for the unconstrained minimization of nonconvex differentiable functions. In particular, we show that with this line search every limit point produced by the Polak-Ribiere iteration is a stationary point of the objective function. Moreover, we define adaptive rules for the choice of the parameters in a way that the first stationary point along a search direction can be eventually accepted when the algorithm is converging to a minimum point with positive definite Hessian matrix. Under strong convexity assumptions, the known global convergence results can be reobtained as a special case. From a computational point of view, we may expect that an algorithm incorporating the step-size acceptance rules proposed here will retain the same good features of the Polak-Ribiere method, while avoiding pathological situations. (C) 1997 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.