谱共轭梯度法是经典共轭梯度法的一种重要推广,是求解大规模无约束优化问题的有效方法之一, 其中谱参数的设计尤为重要。本文通过构造一个新的谱参数且要求共轭参数满足一定条件,建立一个新的谱共轭梯度法框架。常规假设条件下,使用强Wolfe非精确线搜索准则产生步长,证明新算法框架具有充分下降性及全局收敛性。最后,基于新算法框架, 选择满足条件的现有共轭参数进行数值测试,并与其他数值效果较好的算法进行比较,结果显示基于本文新算法框架所建立的算法是有效的。
The spectral conjugate gradient method is an important extension of the conjugate gradient method, and is one of the effective methods for solving large-scale unconstrained optimization. The designing for the spectral parameter is a critical work in spectral conjugate gradient method. In this paper, a new spectral parameter is given, and a new framework of spectral conjugate gradient method is established when the conjugate parameter satisfies a certain restrictive condition. Under the general assumptions and in case where the strong Wolfe inexact line search criterion to yield the step length, the new algorithm framework have sufficient descent property and global convergence. Finally, for the new algorithm framework, the existing conjugate parameter that satisfies the restrictive condition is selected, and the numerical experiments are done to compare the proposed algorithm with other potential algorithms, and the numerical results show that the established algorithm is promising.
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