一种含参数的修正HS共轭梯度法及其收敛性

A modified HS conjugate gradient method with parameter and its convergence

提出了一种含参数的修正HS共轭梯度法,该算法具有性质:1参数βBHSk不仅具有梯度值的信息还具有函数值的信息;2参数βBHSk是非负的;3其产生的搜索方向是充分下降的。在合适的条件下,证明了该算法在弱的Wolfe线搜索下具有全局收敛性,数值结果证明了该算法对于求解无约束优化问题的有效性。

A modified HS conjugate gradient method is proposed, which has the following proper-ties：①The parameter βBHSk has not only gradient value information but also function value informa-tion;②The parameter βBHSk ≥0; ③The search direction of this method possesses the sufficient de-scent property. Under suitable conditions, it is proved that the proposed method with weak Wolfe line search is globally convergent. The numerical results show that the proposed method is effective for solving unconstrained optimization problems.