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β_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.
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 formulaβk,the new algorithm satisfies descent conditions naturally.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.
出处
《运筹学学报》
CSCD
2010年第3期122-128,共7页
Operations Research Transactions
基金
国家自然科学基金项目(60972140)资助
关键词
运筹学
无约束最优化
混合共轭梯度法
强WOLFE线性搜索
全局收敛性
Operations research
unconstrained optimization
hybrid conjugate gradient
strong Wolfe line search
global convergence
