一种修正的DY共轭梯度法及全局收敛性

A modified DY conjugate gradient method and its global convergence

为寻求同时具有良好的收敛性和数值表现的共轭梯度法,在Wolfe线搜索下,构造一种修正的DY共轭梯度法.该算法产生的搜索方向为充分下降方向,这一性质与所采用的线搜索方法无关.在Wolfe线搜索的条件下证明该算法具全局收敛性.研究结果表明:算法是有效的,尤其对大规模无约束优化问题.

In order to find a good convergence and numerical expression of conjugate gradient method at the same time, a modified DY conjugate gradient method （NMDY） is proposed under general Wolfe line search. This method can generate sufficient descent direction for the objective function, at the same time this property is independent of the line search method used. Global convergence of new methods under Wolfe line search is proved. Numerical experiment results show that the algorithm is effective, especially for a large-scale unconstrained optimization problem.