一个自适应Dai-Liao共轭梯度法

An Adaptive Dai-Liao Conjugate Gradient Method

共轭梯度法是求解大规模无约束优化问题的经典方法之一.基于搜索方向矩阵的谱条件数,给出了一个Dai-Liao(DL)共轭梯度法中参数的自适应形式,提出一种自适应DL共轭梯度算法.在适当的条件下,对于一致凸的目标函数证明了该方法具有全局收敛性.数值结果表明,提出的方法是可行的.

The conjugate gradient method is one of the classical methods for solving large-scale unconstrained optimization problems.Based on spectral condition number of the search direction matrix,an adaptive version of parameter of Dai-Liao(DL)conjugate gradient method is presented,and the adaptive DL conjugate gradient algorithm is proposed.Under some mild assumptions,the global convergence of the proposed method is proved for uniformly convex objective functions.Numerical experiments show that the proposed method is promising.