一个修正PRP共轭梯度法的全局收敛性

Global Convergence of a Modified PRP Conjugate Gradient Method

中文关键词:  无约束优化  对共轭梯度法  全局收敛.

英文关键词:unconstrained optimization  conjugate gradient method  global convergence.

中文摘要:

      对于求解无约束优化问题的共轭梯度法,本文提出了一个关于$\beta^{{\rm PRP}}_k$的修正公式.该公式保持非负性,这个性质与线性搜索无关.在适当的条件下我们证明了相应修正PRP共轭梯度法对强Wolfe-Powell线性搜索是全局收敛的.数值结果表明该方法是有效的.

英文摘要:

      In this paper, a modified formula for $\beta _k^{{\rm PRP}}$ is proposed for the conjugate gradient method of solving unconstrained optimization problems. The value of $\beta _k^{{\rm PRP}}$ keeps nonnegative independent of the line search. Under mild conditions, the global convergence of modified PRP method with the strong Wolfe-Powell line search is established. Preliminary numerical results show that the modified method is efficient.