求解无约束优化问题的两个谱共轭梯度法的全局收敛性

Global Convergence of Two Spectral Conjugate Gradient Methods for Unconstrained Optimization

谱共轭梯度法含有两个方向调控参数,是一种结合共轭梯度法和谱梯度法的无约束优化方法。本文建立新的共轭参数和谱参数,提出无约束优化问题的两个谱共轭梯度法,这两个新方法在精确线搜索下等价于FR共轭梯度法。然后,证明了算法1在Wolfe线搜索下和算法2在Armijo线搜索下的全局收敛性,并给出了算法的数值实验结果,验证了算法的有效性。

Spectral conjugate gradient method contains two directions regulatory parameters is a kind of method for unconstrained op- timization that combines conjugate gradient method with spectral gradient method. In this paper, based on the new conjugate param- eters and spectral parameters, two spectral conjugate gradient methods are proposed; the corresponding methods are equivalent to the FR conjugate gradient method when the line search is exact. Moreover, the global convergence of algorithm 1 with Wolfe line search is proved, the global convergence of algorithm 2 with standard Armijo line search is proved. The given numerical results show that the new methods are efficient.