The convergence of conjugate gradient method with nonmonotone line search
The convergence of conjugate gradient method with nonmonotone line search
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DOI：
10.1016/j.amc.2010.06.047
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发表时间：
2010-11
期刊：
影响因子：
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通讯作者：
Zhenjun Shi;Shengquan Wang;Zhiwei Xu
中科院分区：
文献类型：
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作者：
Zhenjun Shi;Shengquan Wang;Zhiwei Xu
共轭梯度法是求解大规模极小化问题的一种有效方法。Liu和Storey发展了一种共轭梯度法，它具有良好的数值性能，但在传统的线搜索（如Armijo线搜索、Wolfe线搜索和Goldstein线搜索）下不具有全局收敛性。本文对Liu-Storey共轭梯度法提出了一种新的非单调线搜索。这种新的非单调线搜索能保证LS方法的全局收敛性，并具有良好的数值性能。通过估计目标函数导数的Lipschitz常数，我们可以找到一个适当的步长，并大大减少了每次迭代的功能评估的数量。数值计算结果表明，该方法在实际计算中是有效的。
The conjugate gradient method is a useful and powerful approach for solving large-scale minimization problems. Liu and Storey developed a conjugate gradient method, which has good numerical performance but no global convergence under traditional line searches such as Armijo line search, Wolfe line search, and Goldstein line search. In this paper we propose a new nonmonotone line search for Liu-Storey conjugate gradient method (LS in short). The new nonmonotone line search can guarantee the global convergence of LS method and has a good numerical performance. By estimating the Lipschitz constant of the derivative of objective functions in the new nonmonotone line search, we can find an adequate step size and substantially decrease the number of functional evaluations at each iteration. Numerical results show that the new approach is effective in practical computation.