摘要:共轭梯度法是求解非线性无约束优化问题的一种重要方法，尤其适用于求解大规模优化问题. 本文提出了一种新的共轭梯度法. 对任意的线性搜索，该方法都满足充分下降条件. 同时，在Armijo型线搜索下，该算法具有全局收敛性.
关键词：共轭梯度法；无约束优化问题；全局收敛性；Armijo型线搜索
ABSTRACT:Conjugate gradient method is a kind of important method for solving the nonlinear unconstrained optimization problem. It is especially suitable for solving large-scale optimization problem. This paper presents a new conjugate gradient method. The method always generates sufficiently descent direction independent on the line search be used. At the same time, we prove that the method proposed in this paper is global convergence with Armijo type line search.
Keywords: conjugate gradient method; unconstrained optimization problem; global convergence; Armijo type line search
目前求解无约束优化问题有很多方法，比如最速下降法、牛顿法、拟牛顿法和共轭梯度法.在这些方法中，共轭梯度法是求解大规模无约束优化问题的有效方法之一.
本文提出了求解无约束优化问题的一种新的共轭梯度法.对任意的线搜索，该方法都满足充分下降条件.该方法在Armijo型线搜索下，具有全局收敛性，说明该方法具有一定的有效性.
