Armijo型线搜索下一种共轭梯度法的收敛性

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。

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

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 suffcient 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.