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运筹学学报 ›› 2010, Vol. 14 ›› Issue (3): 122-128.

• 运筹学 • 上一篇    

推广AS-GN混合共轭梯度算法

闫晖, 陈兰平   

  • 出版日期:2010-09-15 发布日期:2010-09-15

Extended AS-GN Hybrid Conjugate Gradient Method

YAN Hui, Chen-Lan-Ping   

  • Online:2010-09-15 Published:2010-09-15

被引次数

9

摘要： 本文提出了一种求解无约束优化问题的新算法,使Touati-Ahmed, Storey提出的混合共轭梯度法(以下简称AS)和Gilbert, Nocedal提出的混合共轭梯度法(以下简称GN)成为新算法在精确线性搜索下的特例.通过构造新的$\beta_{k}$计算公式,新算法自然满足下降性条件,且这个性质与线性搜索和目标函数的凸性均无关.在一般的条件下,我们证明了新算法的全局收敛性.数值结果表明该算法对测试函数是有效的.

Abstract: In this paper, we propose a new algorithm for unconstrained optimization.It makes  Touati-Ahmed and Storey's  and Nocedal and Gilbert's hybrid conjugate gradient methods to be special cases under precise line search.From the construction of the new formula $\beta_{k}$, the   new algorithm satisfies descent  conditions turally. And this property depends neither on the line search used nor on the convexity of the objective function.Under normal conditions, we prove the new method  can ensure the global convergence. Numerical results also show its efficiency.