Armijo型线搜索下一种共轭梯度法的收敛性

Convergence Properties of a Conjugate Gradient Method with Armijo-type Line Searches

对无约束非线性规划问题,本文分别在两种不同的Armijo型线搜索下证明了Liu-Storey共轭梯度法的所有搜索方向都是充分下降的,并进一步证明了该算法是全局强收敛的。对另一种放松了函数值下降条件可以获得更大步长的Armijo型线搜索,本文还证明了该算法是全局强收敛的。

This paper considers the Liu-Storey conjugate gradient algorithm for unconstrained optimization. Under two different Armijo-type line searches, we show that the search direction generated by the algorithm at each iteration satisfies the sufficient descent condition. Further, we prove that the algorithm is strongly globally convergent. For another Armijo-type line search, which relaxes the function condition and allows bigger steplengths, we also prove the strong convergence of the algorithm.