一种新线性搜索下的混合共轭梯度法

A Mixed Conjugate Gradient Method under a New Linear Search

共轭梯度法是求解大规模无约束问题的一种有效方法,文章针对算法的优劣主要依赖于步长因子和搜索方向的特点,结合共轭梯度法的共轭性质,在HS方法和DY方法的基础上,提出了一种混合共轭梯度法,并证明了全局收敛性。

Conjugate gradient method is an efficient method in solving large-scale unconstrained problems. In light of the fact that the advantage or disadvantage of an algorithm is more or less determined by the step size and the search direction of the algorithm, combined with the conjugate feature of conjugate gradient method, a mixed conjugate gradient method is proposed based on Hestenes-stiefel Algorithms and Dai-Yuan Algorithms. Meanwhile, this method has been proved to ensure the global convergence under a new linear search.