一类具有全局收敛性质的共轭梯度法

非线性共轭梯度法由于其迭代简单和储存量小,且搜索方向不需要满足正割条件,在求解大规模无约束优化问题时占据及其重要的地位.提出了一类新的共轭梯度法,其搜索方向是目标函数的下降方向.若假设目标函数连续可微且梯度满足Lipschitz条件,线性搜索满足Wolfe原则,讨论了所设计算法的全局收敛性.

A New Class of Nonlinear Conjugate Gradient Methods with Global Convergence Properties

Nonlinear conjugate gradient methods have played an important role in solving large scale uncon- strained optimization problems, it is characterized by the simplicity of their iteration and their low memory requirements. It is well-known that the direction generated by a conjugate gradient method may be not a de- scent direction. In this paper, a new class of nonlinear conjugate gradient method is presented, its search di- rection is a descent direction for the objective function. If the objective function is differentiable and its gradi- ent is Lipschitz continuous, the line search satisfies strong Wolfe condition, the global convergence result is established.