一个充分下降LS型共轭梯度算法的全局收敛性

The convergence property of a sufficient descent LS-type conjugates gradient method

共轭梯度法是求解大型无约束非线性优化问题的一种常用方法,在应用中通常以负梯度方向作为其自动重启方向.该文在LS共轭梯度法的基础上,结合一种新的自动重启方向,证明了算法的自动充分下降性和在强Wolfe线搜索下的全局收敛性,给出的数值试验结果表明算法是有效的.

The conjugate gradient method is a common method for solving large-scale unconstrained nonli rectlon IS usua near optimization problems, and in practice, the negative gradient diused as the automatic restart direction. In this paper, based on the LS conjugate gradient method and a new automatic restart direction, the corresponding algorithm is demonstrated to possess the property of automatically generating sufficient descent and the global convergence of the search in strong Wolfe line. The given numerical results show that the proposed algorithm is efficent.