Sufficient descent directions in unconstrained optimization
Sufficient descent directions in unconstrained optimization
复制标题
DOI：
10.1007/s10589-009-9268-z
复制
发表时间：
2011-04
影响因子：
2.2
通讯作者：
Xiaomin An;Donghui Li;Yunhai Xiao
中科院分区：
文献类型：
--
作者：
Xiaomin An;Donghui Li;Yunhai Xiao
下降性是迭代法全局收敛的重要条件。在本文中，我们提出了一种方法来构造无约束优化的充分下降方向。然后，我们应用该技术来获得一个PSB（Powell-Symmetric-Broyden）为基础的方法。基于PSB的方法局部地简化为具有单位步长的标准PSB方法。在适当的条件下，我们证明了在Armijo线搜索或Wolfe线搜索下，基于PSB的方法对于一致凸问题是全局收敛的和超线性收敛的。我们还做了一些数值实验。结果表明，基于PSB的方法与标准BFGS方法相比具有竞争力。
Descent property is very important for an iterative method to be globally convergent. In this paper, we propose a way to construct sufficient descent directions for unconstrained optimization. We then apply the technique to derive a PSB (Powell-Symmetric-Broyden) based method. The PSB based method locally reduces to the standard PSB method with unit steplength. Under appropriate conditions, we show that the PSB based method with Armijo line search or Wolfe line search is globally and superlinearly convergent for uniformly convex problems. We also do some numerical experiments. The results show that the PSB based method is competitive with the standard BFGS method.