一种具有充分下降性的三项共轭梯度法

A Three-Term Conjugate Gradient Method with Sufficient Descent Property

提出了一种带两个参数的三项共轭梯度法,新算法具有如下特点:1)满足共轭性条件;2)自动具有充分下降性;3)新的搜索方向具有更大的下降量.在合适的条件下,证明了算法在强Wolfe线搜索下具有全局收敛性.最后对新算法进行了数值实验,结果表明算法对求解无约束优化问题是有效的.

In this paper,a three-term conjugate gradient method with two parameters is proposed,which has the following properties:1)The presented method satisfies the conjugacy condition;2)The method possesses the sufficient descent property;3)The search direction of this method has a larger descent.Under mild conditions,the proposed method with strong Wolfe line search technique has been proved to be globally convergent.Some elementary numerical experiments are reported,which show that the proposed method is more effective than some other conjugate gradient methods for solving unconstrained optimization problems.