一类充分下降的混合CD-LS共轭梯度法

A Class of Sufficiently Descending Hybrid CD-LS Conjugate Gradient Methods

为了结合共轭下降(conjugate descent,CD)法良好的理论性质和Liu-Storey(LS)法较好的数值效果,以降低小步长对迭代的不良影响,以及使搜索方向的下降性独立于线搜索的选择。通过混合CD法和LS法的分子,对梯度函数进行了相应的修正。方向的充分下降性独立于线搜索的选取,可应用于多种线搜索;基于Wolfe线搜索,证明了算法的全局收敛性。42类无约束测试函数和图像去噪的结果表明,基于相同的终止条件所提出的算法的迭代次数和迭代时间均少于之前的3类共轭梯度算法。

In order to combine the good theoretical properties of Conjugate Descent(CD)method and the good numerical effect of Liu-Storey(LS)method,it is necessary to reduce the adverse effect of small steps on iteration,and make the decline of search direction independent of the selection of line search.By mixing the molecules of the CD method and the LS method,the gradient function was modified accordingly.The sufficient descent of direction is independent of the selection of line search and can be applied to a variety of line searches.Based on the Wolfe line search,the global convergence of the algorithm is proved.The results of 42 classes of unconstrained test function and image denoising show that based on the same termination conditions,the number of iterations and iteration time of the proposed algorithm are lower than those of the previous three types of conjugate gradient algorithms.